Question

Consider a bob attached to a vertical string. At t = 0, the bob is displaced to a new position where the string makes -8° with the vertical and is then released from rest. If the angular displacement θ(t) is written as a cosine function, then the phase constant φ is:

Answer 1

The cosine law of motion will have the following view:

$$\theta (t) = \theta_0 \cos(\omega t+\phi)$$

where $\theta_0 =8\degree$ is the magnitude and $\phi$ is the phase constant. The meaning of this constant is the phase at the initial moment of time. Thus, substituting $t=0$ in the equation, get:

$$\theta (0) = 8\degree \cos\phi = -8\degree\\ \cos\phi = -1\\ \phi = 180\degree$$

Answer. 180 degrees.