A pendulum clock is a clock that uses a swinging weight (a pendulum) as its

time-keeping element. At t=0 s, the pendulum is 5 cm to the right of the

resting position (+5 cm). At t = 2 s, the pendulum is 5 cm to the left of the

resting position (-5 cm).

a) Determine the equation of the sinusoidal function that describes the distance

of the pendulum from its resting position in terms of time.

Answer: x (t) = 5cm*cos (t*pi/2s)

Step-by-step explanation:

This is a sinusoidal equation, so we can write this as:

x (t) = A*cos (c*t + p) + B

where B is the axis around the movement, as the resting position is x = 0, we have B = 0

so x (t) = A*cos (c*t + p)

A is the amplitude of the oscilation, c is the frequency and p is a phase.

We know that when t = 0s, we have x (2s) = 5cm

if this is the maximum displacement, then knowing that the maximum of the cosine is cos (0) = 1

then we must have that p = 0

x (0s) = A*cos (0) = 5cm

then we have A = 5cm

Now, when t = 2s, we have:

x (2s) = 5cm*cos (2s*c) = - 5cm

then 2s*c is the minimum of the cos (x) function, this is:

cos (pi) = - 1

then 2s*c = pi

c = pi/2s.

then our function is:

x (t) = 5cm*cos (t*pi/2s)