Question

Consider a small mass performing simple harmonic motion with angular frequency 10rad/s. If we know that at t = 0 the mass is at x0 = +5cm moving to the right at +87cm/s, and we want to represent the oscillations using a cos function then ... (a) Find the amplitude of the oscillations (b) Find the phase constant of the oscillations (c) Find the maximum speed of the mass (d) Find the maximum acceleration of the mass

Answer 1

Option (b) is correct
The general formula for the amplitude is,
x = A cos(t + C)                      ...(1)
Where A is the amplitude, is the angular frequency and C is the phase constant.
Given that at time, t = 0, x = 5 cm
5 = A cos(0 + C)
A cosC = 5            ...(2)

Differentiating equation (1),
dx/dt = v = A sin(t + C)
At t = 0, v = 87 cm/s
87 = A x 10 sinC
A sinC = 8.7       ...(3)

(3)/(2) gives
tanC = 8.7/5 = 1.74
C = 1.05 rad