Shm Definition and 502 Threads

Homework Statement This problem relates to a mass on a spring, or most any SHM. For an undamped free vibration, I can solve the problem and reduce it to this equation: l = Acoswt + Bsinwt (1) I know the equation is correct. I also know that the above equation reduces to: Rcos(wt -\delta)...

Hi, I have a question: What happens when: We add increase the mass on a spring, displace it as much as we did with a lighter mass and allow it to oscillate. Would the period remain the same? In the end, the force was increased when displacing and the maximum displacement was kept...

Hi, :smile: As I was going through some SHM problems I came across a doubt regarding normal forces. Let's use as an example a book standing on a table: There are two forces acting on the book: It's weight acting downwards and a normal reaction force from the table acting upwards. My doubt...

The frequency and the period of Simple harmonic motion don't depend on the amplitude. Meaning that changing the amplitude of a simple harmonic oscillator doesn't affect its frequency.. amplitude is the max displacement. Doesn't it make sense that if the max displacement is larger, then time...

Which of the following is not essential for SHM? a) restoring force b) gravity c) elasticity d) inertia

Hi, I am learning trigonometric graphs and transformations as I am learning my SHM equations and I have a doubt: Firstly, I have a hard time defining angular frequency and that might be one of the sources of my problem. Can anyone help me with that? Is it simply how many full, 2pi rotations it...

Hi :smile: I am a bit lost with the equations for velocity: I don't know Calculus yet, so my teacher just gave me the equation: -wx0cos(wt) (w being omega) He then said: v0 = wx0 and therefore, concluded: -v0cos(wt) and then for when the displacement is maximum at time = 0: v0cos(wt) Is...

Hi, I am learning about SHM and in order to explain why the acceleration is proportional to the displacement but in opposite directions the book used as an example a particle with mass m, attached to a spring. He defines the displacement to the right as being positive and to the left as...

Hi, As part of my SHM lessons, I got this sheet today to study Phase Difference. I tried drawing what was asked and I have the impression I got the first two graphs correct. However, I am in doubt regarding the third, mostly I guess, with differentiating what is meant by ahead and behind...

Homework Statement The Attempt at a Solution Please tell me how will there be an SHM?

Hi, I just learned my first equation today in SHM: x = xo cos (ω * t) Firstly, is it ok if I change the "x =" part for a "y="? I get a bit confused since, from what I understand, we want to find the vertical distance from the x-axis and that would be the y output of a function. (x makes...

So, in lectures we derived the equation for damped SHM by solving the differential equation relating position (x), mass (m), spring constant (s), and damping coefficient (r): m\ddot{x}=-\frac{s}{m}x-r\dot{x} Using a solution of the form Ae^{\alpha t}, we find that: x=Ae^{-pt}e^{\pm qt}...

Homework Statement If the axis of rotation of a physical pendulum is placed closer to the COM, is the period of rotation longer? If it originally starts .5m from the COM the moves .3M from the COM the peroid shoud be longer right? I keep getting a longer period when the axis of roatation is...

Hey there, The Question Points A,B,C,D, and E lie in a straight line. AB=BC=15 cm, CD=10 cm and DE=20 cm. A particle is moving with SHM so that A and E are the extreme positions of its motion. The period of the motion is 0.2s. Find the time the particle takes to get from B to D i) if it is...

Homework Statement A spring of unstretched length L0 = 60.5 cm and spring constant K is suspended vertically as shown. A mass m is attached to the spring and it stretches the spring to a length of 123 cm. Then the mass is pulled down an additional 8.74 cm from the equilibrium position and...

Homework Statement The displacement of the mass in a mass-spring system is given by the expression x(t) =(0.120 m) sin(1.73 t). What is the maximum velocity of the mass?* 
A.* 0.348 m/s 
B.* 0.307 m/s
 C.* 0.256 m/s 
D.* 0.208 m/s 
E.* 0.175 m/s* Homework...

I am asked to derive a formula from the diagram attached. I should end up with this equation: f=1/2\pi (k/(M+I/R^2)) I tried really hard relating linear quantities with rotational (T=Fr, T=I*alpha etc.) ones but it was all in vain. Any help would be really appreciated. thanks

Homework Statement A uniform sphere of radius a is placed at the lowest point of a fixed thin hemispherical bowl of radius b > a. The sphere is the slightly displaced and released with zero initial velocity such that it rolls without slipping on the inner surface of the bowl. By...

Homework Statement Two identical atoms in a diatomic molecule vibrate as harmonic oscillators. However, their center of mass, midway between them, remains at rest. 1)Show that at any instant, the momenta of the atoms relative to the center of mass are p and -p 2)Show that the total...

Homework Statement [PLAIN]http://img848.imageshack.us/img848/1150/damped.png Homework Equations The Attempt at a Solution Part i) x(t) = C1coswt + C2sinwt dx/dt = -C1wsinwt +C2wcoswt using IC's: xo = C1 dxo/dt = C2w therefore x(t) = xocoswt + (dxo/dt)/w sinwt but...

Homework Statement A uniform beam is suspended horizontally by two identical vertical springs that are attached between the ceiling and each end of the beam. The beam has mass 225 kg, and a 175-kg sack of gravel sits on the middle of it. The beam is oscillating in SHM, with an amplitude of 40.0...

The sun is setting and shines light in such a way that it is directly behind a merry go round, so its shadow is projected onto a wall behind it. The merry-go-round is one where the horses move up and down vertically as they move around the circle. The amplitude of this is 0.5m, and the period of...

there is buoy bobbing gently on the open sea. we need to find 1) average density 2) natural frequency 3) amplitude when the buoy is struck by a wave 4m high (peak to trough) with period 5sec. I've worked out parts 1 and 2: \rho_B = \rho_w \frac{h}{H} (h = height submerged, H= total height)...

Homework Statement A charge +q of mass m is free to move along the x axis. It is in equilibrium at the origin, midway between a pair of identical point charges, +Q, located on the x axis at x = +b and x = -b. The charge at the origin is displaced a small distance x << a and released. Show that...

Homework Statement I've been given (or have calculated) the equation for damped SHM of a spring, and have been told to calculate the period... I'm given that: Forced produced by damper: b(dx/dt) where b = 16N/ms k = 344.5N/m m = 2kg Homework Equations I know that T = 2*pi/(W0)...

Homework Statement I'm looking for a good SHM / Circular Motion applet. Homework Equations N/A The Attempt at a Solution My professor had shown us an applet that had a hanging mass on a spring and a circle in the same applet... Really helped us understand the inter-relationship...

Homework Statement [PLAIN]http://img24.imageshack.us/img24/2706/64505257.jpg Homework Equations t = 2pi * Sqrt(m/k) The Attempt at a Solution Im not very sure how to proceed with this one. I have tried calculating the peroid for 2 separate cases and then adding them together...

Homework Statement A clock pendulum oscillates at a frequency of 1.5 Hz. At t = 0, it is released from rest starting at an angle of 20° to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at the following times? (Hint: Do not confuse the angle of swing θ of...

Homework Statement A 94.0 kg man climbs onto a car with worn out shock absorbers and this causes the car to drop down 5.90 cm and comes to equilibrium. As he drives along, he hits a bump, and this starts the car oscillating at an angular frequency of 4.65 rad/s. What is the mass of the car...

Time period of SHM ! ellloO ^.^ Homework Statement <Q>A particle executes SHM under the restoring force provided by a spring. The time period is T . If the spring is divided in 2 equal parts and one part is used to continue the SHM, The time period will <A> remain T <b> become T/2 <c>...

elllllo :D Homework Statement <q> <Q>A particle is subjected to 2 simple harmonic motions in the same direction having equal amplitudes and equal frequency. If the resultant amplitude is equal to the individual motions,find the phase difference between the individual motions. Homework...

Homework Statement A block having mass m and charge + Q is connected to a spring having constant k. The block lies on a frictionless horizontal track, and the system is immersed in a uniform electric field of magnitude E, directed as shown in Figure P25.11. If the block is released from rest...

Hi all, The textbook simple harmonic oscillator solution has no imaginary values. True or false? If true, why not? Most of the time you get something like XXX.exp[i(Et-p.x)]. I thought maybe it was a superposition of states such that the complex parts cancel, but in that case they'd both...

Homework Statement This is another question related to the vertical spring lab where we try to determine k, the spring constant. When the vertical mass-spring system is at equilibrium, then the F in F = kx is equal to F = mg, or 9.8. What would the F be in F = kx when the system is...

Homework Statement The position of a particle is given by the expression x=4.00 cos (3.00\pit+\pi) where x is in meters and t is in seconds. Determine the frequency, period of the motion, amplitude of the motion, the phase constant, and the position of the particle at t=0.250 s. **I don't...

Lab report help In our lab, we are trying to verify the properties of SHM using a mass spring system. (Verify that amplitude and angle do not matter). We based it on T = 2pi*sqrt(m/k) One system is the vertical one and the other is on an inclined plane. We graphed mg vs. x and T2 vs m and...

Homework Statement View the Earth as a homogenous sphere with the density \rho. Assume a hole has been succesfully been drilled through the center of the Earth, and a body with mass m is dropped down the hole. Give an expression of the force as function of of the distance r from the Earth's...

Homework Statement Our lab was to find the spring constant of the springs that we were using, and then verify the properties of SHM. We used a vertical spring system AND an inclined spring system. We used 3 different springs for both systems. For the vertical system: We hung the 3...

Homework Statement An ultrasonic transducer, of the type used medical ultrasound imaging, is avery thin disk (m=0.10 g) driven back and forth in SHM at 1.0 MHz by an electromagnetic coil. a. The maximum restoring force that can be applied to the disk without breaking it is 40,000 N...

1. What is the amplitude of the pendulum's motion, in meters? (see attached graph) Given: angular frequency=1.26rad/s 2. T=2pi(L/g)^.5; a=-w^2(x); s(t)=Acos(wt+phase); theta=s/L 3. I almost don't even know how to start.. The confusing part I believe is the graph. The max angle...

Homework Statement In a simple atomic model of a solid, the atoms vibrate with a frequency of 2E-11 Hz. The amplitude of the vibration of the atoms is 5.5E-10 m and the mass of each atom is 4.8E-26. Calculate the total energy of the oscillations of an atom. Homework Equations total...

Homework Statement Let a particle slides in a straight smooth tube passing obliquely through the Earth. Assuming no friction and no rotational effects. Describe the motion. Find Frequency and Period. Homework Equations F = -GMm/r^2 The Attempt at a Solution Don't know how to...

SHM on a cylindrical trough (solved?) Homework Statement A solid sphere of radius R rolls without slipping in a cylindrical trough of radius 5R. Show for small displacement, the sphere executes SHM with period T=2\pi \sqrt{\frac{28R}{5g}}...

Hi everyone I'm having trouble using the equations for SHM calculations. We got told to set them on radians but I forgot to when I was doing the problems and got some of the answers right. But when I tried to do them when the calculator was set in radians, the answers were totally wrong...

Homework Statement An atom of mass m is bonded to surface immobile body by electromagnetic forces. The force binding the atom to the surface has the expression: F= exp\ (a\cos z + b\sin z) + d\tan(z) where a,b, and d are constants and z is upwards. The equilibrium point is defined to be...

Homework Statement A particle undergoes simple harmonic motion in both the x and y directions simultaneously. Its x and y coordinates are given by: x=asin(wt) y=bcos(wt) . Show that the quantity x(dy/dt) - y(dx/dt) is constant around ellipse, and what is the physical meaning of this quantity...

Homework Statement A disk of mass M, attached to a spring of constant k fixed to a vertical wall can oscillate freely in a frictionless horizontal plane. A small block of mass m is put on the disk with which there is friction under a coefficient of friction \mu. What is the maximum amplitude...

Homework Statement Two masses m1 and m2 are joined by a light spiral spring. Each body oscillates along the axis of the spring, which obeys Hooke's law in both extension and compression. The bodies move in opposite directions and the centre of mass of the system is stationary. Explain why the...

Hello. I am studying second-order differential equations, and I am currently studying simple harmonic oscillations, like those in a spring-block system. When solving the differential equation, I get answers in the form of y^2= x(t)^2=(c_1^2+c_2^2)(cos^2(\omega...

Homework Statement A uniform meter stick is hung at its center from a thin wire. It is twisted and oscillates with a period of 5 s. The meter stick is then sawed off to a length of 0.76 m, rebalanced at its center, and set into oscillation. With what period does it now oscillate...