Question

The angle that a swinging simple pendulum makes with a vertical obeys the equation $\Theta (t) = (0.150 rad)cos[(2.85 rad/s)t + 1.66]$ where the length of the pendulum is 1.207m.

a. what is the vertical distance (in cm) between the pendulum bob's highest and lowest positions?

b. what is the pendulums max angular speed and max angular accleration?

c. what is the pendulum bob's speed (in m/s) at it's lowest position?

Answer 1

a)

maxm angle = 0.15 rad = 8.59 degree

maxm height = 1.207 (1-cos8.59) = 0.0135m

h = 1.35cm

b)

maxm angular speed w = 0.15x2.85 = 0.4275rad/s^2

maxm angular acceleration = 0.15x2.85x2.85 = 1.218 rad/s^2

c)

speed = Lw = 1.207x 0.4275

v = 0.5159m/s