## Question

###### 12 8) (10 pts) Inspired by donuts, I decided to make a clock. The I0 9...

## Answers

(8) My clock will be running

fast.According to given picture, it shows that the pendulum for my clock is made of donut which attached to the end of a stick. In this picture, i think that pendulum looks running fast.

Using a formula, we have

T = 2

_{}L / gwhere, L = length of a stick = 0.2 m

g = acceleration due to gravity = 9.8 m/s

^{2}then, we get

T = (6.28 rad)

_{}[(0.2 m) / (9.8 m/s^{2})]T = (6.28 rad)

_{}0.0204081 s^{2}T = [(6.28 rad) (0.1428 sec)]

T = 0.896 sec(9) An expression for damped simple harmonic motion which will be given below as -

x (t) = A e

^{-bt/2m}cos (t +_{})An object oscillates in the manner which is described by -

x = (2 m) e

^{-bt/(6kg)}cos { [(2/3) s^{-1}] t }a. If the amplitude of an oscillation is 1 m at time t = 2 sec, then the damping constant of an oscillator will be given by -

(1 m) = (2 m) e

^{-bt/(6kg)}cos { [(2/3) s^{-1}] (2 s) }[(1 m) / (2 m)] = e

^{-bt/(6kg)}cos (4.186 rad)ln (0.5) = - [b t / (6 kg)] (0.9973)

- [(0.6931) (6 kg)] = - b [(2 s) (0.9973)]

b = [(4.1586 kg) / (1.99465 s)]

b = 2.08 kg/s