# Simple harmonic motion/spring

## Homework Statement

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A 1 kg object is connected to a horizontal massless spring. The spring is initially stretched by 0.1m and the object is released from rest there. It proceeds to move without friction. The next time the speed of the object is 0 is 0.5s later.

Determine the maximum speed of the object, the spring constant, and the mechanical energy of the system.

## Homework Equations

T = 2pi(m/k)^1/2

v(t) = -wx sin(wt + phase constant)

w = 2pi/T

## The Attempt at a Solution

Hmm I don't really know where to start with finding the max velocity to be honest. Probably with the second formula I posted, but I'd have to find w first, and I don't know how to find that without T (period) or frequency.

## Answers and Replies

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Hmm I don't really know where to start with finding the max velocity to be honest. Probably with the second formula I posted, but I'd have to find w first, and I don't know how to find that without T (period) or frequency.
The equation for a simple harmonic oscillator is

$$x(t) = Acos(\omega t + \phi)$$

Where

$$\omega = \sqrt{\frac{k}{m}}$$

You should also know that

$$f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$$

$$T = \frac{1}{f}$$

Everything I wrote above is probably given in your textbook.

The equation for a simple harmonic oscillator is

$$x(t) = Acos(\omega t + \phi)$$

Where

$$\omega = \sqrt{\frac{k}{m}}$$

You should also know that

$$f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$$

$$T = \frac{1}{f}$$

Everything I wrote above is probably given in your textbook.
My book says that the velocity for a simple harmonic motion is the derivative of the $$x(t) = Acos(\omega t + \phi)$$

Also, I still don't know where to start as such

max velocity can only be obtained when sin(wt + phase constant) is equal to 1.

that should get you started.

Also think about the position of the object when the speed is equal to 0 and how long it takes to get there. That should help you find the period as well.

OK so I figured that displacement x(t) = A cos (wt)

You know A = .1 m

Solving for w, you can find max speed from vmax = -Aw

But in the equation displacement x(t) = A cos (wt), what are the values for t and x?