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

(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 = 2L / g

where, L = length of a stick = 0.2 m

g = acceleration due to gravity = 9.8 m/s²

then, we get

T = (6.28 rad) [(0.2 m) / (9.8 m/s²)]

T = (6.28 rad) 0.0204081 s²

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