# Simple Harmonic Motion Question (Springs)

• LucasCammarata
In summary, the conversation discusses a 350-g mass attached to a spring with a spring constant of 64 N/m and its maximum acceleration of 5.3 m/s2. The formula used to find maximum acceleration is -w^2[x(t)], which results in a maximum displacement of 0.028984375m. To find the maximum speed, there is a relation between the spring energy at maximum displacement and the kinetic energy when the spring is not exerting a force on the mass.
LucasCammarata
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A 350-g mass is attached to a spring whose spring constant is 64 N/m. Its maximum acceleration is 5.3 m/s2. What is its maximum speed?

So, i had a go at the question which basically required the knowledge that maximum acceleration occurs when displacement is maximum and maximum velocity occurs when displacement is zero.

So, i used the formula that acceleration = -w^2 [x(t)]... getting the result that... 5.3 = -w^2[x(t)] and solved for x(t) using the fact that w^2 = k/m.. therefore getting that maximum displacement = 0.028984375m. Does anyone know where i can go from here to get the maximum speed?

There is a relation between the spring energy when the mass is at its maximum displacement, and the kinetic energy of the mass when the spring is not exerting a force on the mass. Use this.

## What is Simple Harmonic Motion (SHM)?

SHM is a type of periodic motion where an object oscillates back and forth around a central equilibrium point due to a restoring force that is directly proportional to the displacement from the equilibrium point.

## What is a spring constant?

A spring constant, also known as the force constant, is a measure of the stiffness of a spring. It represents the amount of force needed to stretch or compress a spring by a certain length. It is denoted by the letter k and has units of N/m.

## What is the equation for SHM in terms of a spring?

The equation for SHM in terms of a spring is x = A cos(ωt + φ), where x is the displacement from equilibrium, A is the amplitude (maximum displacement), ω is the angular frequency (2π times the frequency), and φ is the phase constant (initial displacement at t = 0).

## How does the mass of an object affect its SHM on a spring?

The mass of an object does not affect the frequency of its SHM on a spring, but it does affect the amplitude and the period. A heavier mass will have a larger amplitude and longer period compared to a lighter mass on the same spring.

## What is meant by the term "period" in SHM?

The period of an SHM on a spring is the time it takes for one complete oscillation (movement from one extreme to the other and back) to occur. It is denoted by the letter T and has units of seconds (s).

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