Simple Harmonic Motion: Calculate Max Velocity

In summary, the conversation discusses a problem involving a mass hanging from a spring and undergoing SHM. The question is to find the speed of the mass when it passes through the equilibrium point, given the mass, spring constant, and starting displacement. The individual attempted to use an equation of motion, but realized it was not applicable due to non-uniform acceleration. They then mentioned using energy conservation as a possible solution method.
  • #1
greenglasses
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Homework Statement


A mass of 0.4 kg, hanging from a spring (k= 80N/m) is set into an up-and-down SHM. What is the speed of the mass when moving through the equilibrium point? The starting displacement, A, is 0.10 m.

Homework Equations


a = -kx/m
ω = 2pi/T

The Attempt at a Solution


I tried to apply one of the equations of motion: 2ax = vf^2 - vi^2: but I got an answer of 2 m/s, which is incorrect as the correct answer is 1.4 m/s. Now, I realize that acceleration is not uniform which means that I can't use that equation.
However, I'm not sure what else to do. Using a = -kx/m I managed to calculate the acceleration at the equilibrium point, but without any sort of time or time period or frequency, I haven't a clue how to solve this question.
 
Last edited:
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  • #2
Use energy conservation.
 

1. What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium, and the motion follows a sinusoidal pattern.

2. How is the maximum velocity of an object in SHM calculated?

The maximum velocity of an object in SHM can be calculated using the formula vmax = √(k/m)A, where k is the spring constant, m is the mass of the object, and A is the amplitude of the motion.

3. What factors affect the maximum velocity in SHM?

The maximum velocity in SHM is affected by the mass of the object, the spring constant of the restoring force, and the amplitude of the motion.

4. Can the maximum velocity in SHM be greater than the velocity at equilibrium?

Yes, the maximum velocity in SHM can be greater than the velocity at equilibrium. This occurs when the object is at its maximum displacement from equilibrium, and is accelerating back towards the equilibrium position.

5. How does the maximum velocity change with different values of mass and spring constant?

The maximum velocity in SHM is directly proportional to the square root of the spring constant and inversely proportional to the square root of the mass. This means that as the spring constant increases or the mass decreases, the maximum velocity will also increase.

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