# Amplitude of oscillation for SHM

• Saptarshi Sarkar
In summary, the mass moves with a velocity of 0.5m/s relative to the elevator when it suddenly stops. The mass starts its oscillation from the centre of SHM with a position of y=0 and a velocity of 0.5m/s. The equation can be simplified by setting y(0) = 0.
Saptarshi Sarkar
Homework Statement
A spring is attached to the roof of an elevator and a mass m is attached to the lower end of the spring. When the elevator is not moving, the mass undergoes a vertical SHM with frequency 2.5rad/s. Now, when the elevator is moving downwards with velocity 0.5m/s, the mass is not undergoing any SHM. Now, if the elevator suddenly stops, what will be the amplitude of oscillation of the mass m?
Relevant Equations
y = ACosωt + BSinωt
From the first part of the question, I was able to get the value of ω which will be the same for the next SHM.

But, I am having difficulties solving for the amplitude as I can't find the boundary conditions required to get the amplitude.

Last edited:
Just before the elevator stops the mass is not moving in the elevator frame. When the elevator stops suddenly how fast is the mass moving relative to the elevator? And, considering it wasn’t oscillating a moment before, what location in the oscillation does it start?

Saptarshi Sarkar
Cutter Ketch said:
Just before the elevator stops the mass is not moving in the elevator frame. When the elevator stops suddenly how fast is the mass moving relative to the elevator? And, considering it wasn’t oscillating a moment before, what location in the oscillation does it start?

When the elevator stops, the mass should move with velocity 0.5m/s wrt the elevator frame. The mass starts moving from the centre of SHM (y=0)

So, that means

y(0)=0
y'(0)=0.5

Is this right?

Yep, where you have defined down as the positive y direction (perfectly acceptable so long as you are consistent through the rest of the calculation)

Saptarshi Sarkar
Also, y(0) = 0 should allow you to simplify your equation.

## 1. What is the amplitude of oscillation for simple harmonic motion (SHM)?

The amplitude of oscillation for SHM is the maximum displacement of an object from its equilibrium position during each cycle of motion. It is a measure of the distance the object moves from its resting point.

## 2. How is the amplitude of oscillation related to the spring constant and mass in SHM?

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

## 3. Can the amplitude of oscillation change over time in SHM?

No, the amplitude of oscillation remains constant in SHM as long as the conditions of the system remain unchanged. This is because SHM is a conservative motion, meaning that energy is conserved and there is no external force acting on the system to change the amplitude.

## 4. How is the amplitude of oscillation affected by damping in SHM?

In SHM with damping, the amplitude of oscillation decreases over time as energy is lost due to frictional forces. The larger the damping coefficient, the faster the amplitude decreases. Eventually, the object will come to rest at the equilibrium position.

## 5. Is there a maximum amplitude of oscillation in SHM?

Technically, there is no maximum amplitude of oscillation in SHM as the displacement can theoretically continue to increase infinitely. However, in practical situations, there are limitations due to factors such as the strength of the material and the length of the spring.

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