# Simple Pendulum amplitude problem

## Homework Statement

A pendulum with a swing amplitude of 150 cm is recorded to have a period of 2.1s. Calculate after 0.3s release from the furthest amplitude position.

a) Angular velocity
b) displacement
c) Angular acceleration
d) Length of the pendulum

I've only had one lecture on circular motion and the motion of pendulums, so I'm a bit unsure of the correct steps for each calculation.

## Homework Equations

$$\omega = \frac{2\pi}{T}$$

$$x = A cos (\omega t)$$

$$a = -\omega^{2}x$$

$$T = 2\pi\sqrt{\frac{l}{g}}$$

## The Attempt at a Solution

a)
$$\omega = \frac{2\pi}{2.1} = 2.99 rad s^{-1}$$

b)
$$x = 1.5 cos (2.99 x 0.3) = 1.5 m$$

c)
$$a = -(2.99)^{2} x 1.5 = -13.41$$

d)
$$l = \frac{T^{2}g}{2\pi^{2}} = 106.74 m$$

I'm not convinced that I'm getting b) right, as it seems odd for the displacement after 0.3 seconds to be the same as the amplitude. This makes me believe that I'm wrong in other places.

See whats wrong? [I dont have the answers to check for myself]

Any similar problems to practice on would be welcomed; I don't want to constantly feel that I'm missing something.

one problem I see is that in part d) you should be dividing by 4, not 2

one problem I see is that in part d) you should be dividing by 4, not 2

also, I do not get the same answer as you do for part b). Make sure your calculator is in radiant, not degrees.

(I am assuming the extra x in the cosine function was a typo)

Oh yes, I think I made a typo when I typed the post; it's 4 PI in my notes. Regardless of that I made a calculation error on that part...

I now have L = 1.1m for d).

Thanks.

Oh yes, I think I made a typo when I typed the post; it's 4 PI in my notes. Regardless of that I made a calculation error on that part...

I now have L = 1.1m for d).

Thanks.

also, check to see if your calculator is in radians. For part B)

Ah... thank you.

Neglected to think that I was working with radians.

b) 0.9 m
c) -8.05

I assume that I've got the right set of answers for the question now.

I think d) is 1.1m.

I was getting 106.74 by forgetting to bracket the 4pi^2; it was dividing by 4 and then multiplying by pi^2. Don't know why, I thought that calculators multiplied before dividing.

I think d) is 1.1m.

I was getting 106.74 by forgetting to bracket the 4pi^2; it was dividing by 4 and then multiplying by pi^2. Don't know why, I thought that calculators multiplied before dividing.

details my friend, details

The physics is the important part.

Thank you for your help; now I can move on and get stuck on something else. Midterm tests next week... :(

Thank you for your help; now I can move on and get stuck on something else. Midterm tests next week... :(

Good luck my friend! may the $$ma$$ be with you