Answer to Question #83288 in Classical Mechanics for prince

Question

The displacement of a particle executing simple harmonic motion is given by x=0.01cos4π(t+0.0625)m. Deduce the period of the motion.
a.1.0 s
b. 0.1 s
c. 2.5 s
d. 0.5 s

Answer 1

The equation of motion for particle executing simple harmonic motion

x=x_max cos⁡〖(ωt+ϕ_0 )=x_max cos⁡(2π/T t+ϕ_0 ) 〗=0.01 cos⁡〖4π(t+0.0625) 〗

Therefore, the period of the motion

T=1/2 s=0.5 s