A particle initially at rest at a distance of 5 cm from its mean position performs a SHM completing 60 oscillations in 2 seconds. Find the equation representing the displacement of the particle at any subsequent instant. What will be its equation if initially the particle were at the mean position?

A particle initially at rest at a distance of 5 cm from its mean posit

1.	A particle initially at rest at a distance of 5 cm from its mean position performs a SHM completing 60 oscillations in 2 seconds. Find the equation representing the displacement of the particle at any subsequent instant. What will be its equation if initially the particle were at the mean position?
Answer» Solution :Time TAKEN by the particle in SHM to complete 60 OSCILLATION = 2 s. `THEREFORE` Time period of the particle, `T=2/60=1/30s`. Angular velocity of the particle, `omega=(2pi)/T=(2pi)/(1/30)=60pi`. The particle was at REST and about 5 CM away from its equilibrium position. `therefore` Amplitude of the particle, a = 5 cm. Let, at any time t, the particle is x cm away from its equilibrium position. `therefore` Displacement of the particle, `x=5cos(60pit+theta)cm` At t = 0, x = 5 cm `therefore" "5=5costhetaor,costheta=1or,theta=0` `therefore" "x=5cos60pit` If the particle starts its oscillation from the equilibrium position, then, `x=5sin60pit`.