Question

A simple harmonic oscillator has amplitude 10 cm and it completes 120 oscillations in 60 Seconds if the initial phase is pi by 2 write expressions for its displacement and velocity

Answer 1

Hey dear,

● Answer -
x = -10sin(4πt) cm
v = -40πcos(4πt) cm/s

● Explaination -
# Given -
A = 10 cm
f = 120/60 = 2 Hz
θ = π/2 rad

# Solution -
Angular velocity of SHM is -
ω = 2πf
ω = 2π×2
ω = 4π rad/s

Displacement of particle in SHM is given by -
x = A.cos(ωt+θ)
x = 10cos(4πt+π/2)
x = -10sin(4πt) cm

Velocity of particle in SHM is given by -
v = Aω.sin(ωt+θ)
v = 10×4πsin(4πt+π/2)
v = -40πcos(4πt) cm/s

Hope this helped you...