What Is the Maximum Speed of the Oscillator?

In summary, the problem involves a mechanical oscillator executing simple harmonic motion. The given information includes the mass of the oscillator (253 g), its speeds at two different displacements (89.28 cm/s at 2.79 cm and 70.95 cm/s at 6.56 cm), and a request for the maximum speed. To solve this problem, we can use the equation x(t) = A*cos(omega*t) + B*sin(omega*t) and plug in the given values to find the values of omega, t, A, and B. However, the student is confused and unsure of where to start, as the textbook did not provide proper explanation or examples for this type of problem.
  • #1
nweis84
16
0

Homework Statement



A 253 g oscillator has a speed of 89.28 cm/s when the displacement is 2.79 cm and a speed of 70.95 cm/s when the displacement is 6.56 cm. What is the oscillator's maximum speed?


Homework Equations





The Attempt at a Solution



well, I haven't really attempted a solution because I'm totally confused on where to start with this problem. I've read the entire chapter and can't come up with any similar examples or formulas that would help solve this because it just doesn't give me enough information.

please help!
 
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  • #2


Presumably this is a mechanical oscillator executing simple harmonic motion?

If that is the case, assume the displacement looks like
x(t) = A*cos(omega*t) + B*sin(omega*t)
and see what you can do to fit the given information.
 
  • #3


Sorry I'm still very confused,
how can we find omega or t or A or B from any of the given information?

my book just doesn't explain at all how to handle this type of problem

and also that's the first time I've seen an equation written that way

I have seen the x(t) = Acos(w*t) and the one with the phase constant phi
 

FAQ: What Is the Maximum Speed of the Oscillator?

What are oscillations?

Oscillations refer to the repetitive movement of an object or system around a fixed point or equilibrium. This movement can be described as a back-and-forth motion, with the object or system crossing the equilibrium multiple times.

What causes oscillations?

Oscillations are caused by a restoring force that acts on the object or system, bringing it back to the equilibrium after being displaced. This restoring force can be gravity, tension, or any other force that tries to bring the object or system back to its original state.

What is the difference between simple harmonic motion and damped oscillations?

Simple harmonic motion refers to the ideal case of oscillations, where there is no resistance or damping force acting on the object or system. Damped oscillations, on the other hand, involve a damping force that reduces the amplitude of the oscillations over time, eventually bringing the object or system to rest.

How can we mathematically describe oscillations?

Oscillations can be described using mathematical equations such as the simple harmonic motion equation: x(t) = A cos(ωt + φ), where x is the displacement of the object or system, A is the amplitude, ω is the angular frequency, and φ is the phase angle.

How can we measure the frequency and period of oscillations?

The frequency of oscillations can be measured by counting the number of oscillations that occur in one second. The period, on the other hand, is the time it takes for one complete oscillation and can be calculated by dividing the total time by the number of oscillations.

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