Answer to Question #126999 in Mechanics | Relativity for alaa

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

Simple harmonic oscillator equation

$x=Acos(\omega t+\phi)$

applying the initial conditions at t=0 the equation reduces to

$-8=A cos(0+\phi)$

$-8=Acos\phi$

$\phi =cos^{-1} (\frac{-8}{A})$