Answer to Question #85519 in Physics for Samita Shukla

Question

A simple harmonic oscillator has amplitude 10 cm and it completes 120 oscillations
in 60 s. i) Calculate its time period and angular frequency. ii) If the initial phase is
π/2, write expressions for its displacement and velocity. iii) Calculate the values of
maximum velocity and acceleration

Answer 1

i)

T=60/120=0.5 s.

The angular frequency

ω=2π/T=2π/0.5=4π rad/s.

ii)

x(t)=A cos⁡(ωt+ϕ)=10 cos⁡(4πt+π/2) =(-10 sin⁡4πt ) cm.

v(t)=1/4π (-10 cos⁡4πt )=(-5/2π cos⁡4πt ) cm/s.

iii)

V=Aω=(10)(4π)=40π cm/s≈1.26 m/s

a=Aω^2=(10) (4π)^2=160π^2 cm/s^2 ≈15.8 m/s^2