Spring block Definition and 27 Threads

The equation of motions looks like $$m\ddot{x}(t)+m\Gamma\dot{x}(t)=-K(x(t)-d_0\cos{\omega_d t})\tag{3}$$ Moving other end of the spring sinusoidally effectively produces a sinusoidally varying force on the mass. Everything written above so far is as presented by the book "The Physics of...

So I proceed as: Total time for 1 oscillation is 0.2s $$\frac{1}{\sqrt{2}}=\sqrt{2} \sin ({\omega t_1})$$ $$\sqrt{2}=\sqrt{2} \sin ({\omega t_2})$$ Therefore $$\omega t_2=\frac{\pi}{2}$$ $$\omega t_1=\frac{\pi}{6}$$ $$\omega ×2(t_1+t_2)=2×\left( \frac{\pi}{2}+\frac{\pi}{6}\right) $$ Since...

I have used the work energy theorem like all source have shown me an have arrived at the right answer where work one by all the forces is the change in kinetic energy -1/2kx^2 - umgcosΘx +mgsinΘx = 0 is the equation which becomes -1/2kx -umgcosΘ+ mgsinΘ = 0 where k= spring constant u=...

A block of mass 0.2 kg which slides without friction on a θ = 30° incline is connected to the top of the incline by a mass-less spring of relaxed length of 23.75 cm and spring constant 80 N/m as shown in the following figure. (a) How far from the top of the incline does the block stop? (b) If...

the acceleration of the center of mass is ##a_{cm} = F/(M+m)## I considered the forces on the block of mass m(when the system is at maximum extension) I got the equation $$kx - \frac {mF}{(M+m)} = ma_{cm}$$ and from that I got the value of the maximum extension $$x = \frac {2mF} {k(M+m)}$$ which...

I found the amplitude of the simple harmonic motion that results (0.367, and I know this is correct because I entered it and it was marked as a correct answer), and assumed it would be the same value for the maximum compression since x(t) = Acos(wt). And, since the maximum value of cosine is 1...

Using conservation of energy, 0.5kx^2=mgh=mgx 0.5kx=mg 0.5kx=mg, x=0.15, m=9, g= 9.8 So isn't it k= 1176N/m? For this problem, I understand that you can't use conservation of energy, but why? There is gravitational potential energy at the top and spring elastic energy at the bottom, and no...

Summary:: A block of mass m is dropped onto the top of a vertical spring whose force constant is k. If the block is released from a height h above the top of the spring, a) what is the maximum energy of the block? b) What is the maximum compression of the spring? c) At what compression is the...

In the given problem, i can understand that after placing the two blocks in equilibrium it oscillates with an amplitude of The answer for (b) is given as To my knowledge, m2 separate from m1 when the acceleration is greater than gsinø and so they should be separating only at max displacement...

Hello everyone! I am trying to replicate a folding machine, just as a fun project for home use. I understand this simple idea of a folding machine, and I know which measurements I should take. The question behind this project that I simply can´t understand is the spring linear clamp which...

Its a very basic problem and my friend suggested a solution that we should equate mg and kx ie mg=kx and just plug in m=8 and x=0.16 but i think that we should equate the energies like mgx=1/2kx^2 ie because at the point where mg will be equal to kx the mass will still have a velocity hence it...

The fig. 1.1(a) is a mass m attached to a spring that is fixed to a wall. I don't understand what does "a sudden momentum impulse" means. Is it an external force o what? I imagined that the new equation of motion would be md^2x/dt^2+dp1/dt-kx=0 md^2x/dt^2+mdv1/dt-kx=0 is this the equation i...

Homework Statement A block is suspended by an ideal spring of the force constant K. If the block is pulled down by applying a constant force F and if maximum displacement of the block from its initial position of rest is X then, find the value of X. Homework Equations mg + F = XK + K(mg/K)...

Homework Statement A block is acted on by a spring with spring constant k and a weak friction force of constant magnitude f . The block is pulled distance x0 from equilibrium and released. It oscillates many times and eventually comes to rest. Show that the decrease of amplitude is the same...

Homework Statement A 20.0 kg block on a horizontal surface is attached to a horizontal spring of k = 2.0 kN/m. The block is pulled to the right so that the spring is extended 10.0 cm beyond its unstretched length, and the block is then released from rest. The frictional force between the...

Homework Statement "Consider a 250 gram block on a 10 degree frictionless incline and in contact with a spring of constant 1.2 N/cm. If the block is launched from rest by the spring with an initial compression of 6cm, how fast is the block moving at the point of release from the spring? How...

Homework Statement A block is attached to the sides of a square box by 4 springs. The box is placed horizontally on a frictionless surface (ignore gravity). The mass of the block is ##m##, the natural length of each spring is ##l##, and the strength of each spring is ##k##. Place the block at...

Homework Statement A block is attached to the sides of a square box by 4 springs. The box is placed horizontally on a frictionless surface (ignore gravity). The mass of the block is ##m##, the natural length of each spring is ##l##, and the strength of each spring is ##k##. Place the block at...

Homework Statement :[/B] The figure shows a pulley block system in equilibrium. If the block is displaced down slightly from its position and released, find the time period of the oscillation. Assume friction is sufficient. I: moment of inertia of pulley k: spring constant R: Radius of pulley...

1. Homework Statement : The block of mass m1 as shown in the figure (pic attached)is fastened to the spring and the block of mass m2 is placed against it. a)Find the compression of the spring in equilibrium position. b)The blocks are pushed a further distance (2/k)(m1 + m2)g sinθ against the...

Just got confused that while applying the Work - Energy Theorem in a vertical Spring-Block system performing SHM (considering no other external forces other than gravity), when I apply the theorem from equilibrium position, do I consider the work done by gravity?

A particle that hangs from a spring oscillates with an angular frequency of 2 rad/s. The spring is suspended from the ceiling of an elevator car and hangs motionless (relative to the car) as the car descends at a constant speed of 1.5 m/s. The car then suddenly stops. Neglect the mass of the...

Homework Statement a block of mass m as shown in figure lies on a smooth horizontal surface and springs are at natural length. when the block is displaced slightly then find the time period of oscillation Homework Equations $$T=2\pi\sqrt{\frac{m}{k}}$$ for series connection of...

Homework Statement The block shown in the drawing is acted by a spring with spring constant ##k## and a weak friction force of constant magnitude ##f##. The block is pulled a distance ##x_0## from equilibrium and released. It oscillates many times and eventually comes to rest. a. Show that the...

Homework Statement A 4kg block M in horizontal plane is attached to a sprig S1 fixed to a light rod OA of length 4m as shown in diagram(refer to attachement). The other end O of the rod is hinged to rotate in the plane about the vertical axis passing through it. A spring S2 is fixed to the mid...

Homework Statement A block A has mass =2kg and is attached to a spring of spring constant=40N/m .Another block of mass 4kg is pressed against A so that the spring is compresses by a distance 'd' .Then find the maximum value of 'd' for which on release of the B does not lose contact from the...

a 1 kg mass attached to a spring with a force constant of 25 oscillates on a horizontal, frictionless track. At time t=0, the mass is released from rest at x=-3cm (the spring is compressed by 3cm). Find (a) the period of its motion. b) the max values of speed and acceleration. c) the...