Question

A particle having mass 10 g oscillates according to the equation x=(2.0 cm).sin[(100 /s)t+π/6]. Find the amplitude, the time period and the spring constant (b) the position, the velocity and the acceleration at t=0.

Answer 1

Given equation of the S.H.M.,

 x = (2.0 cm).sin[(100)t + π/6]

Comparing this equation with x = ASin(ωt + Φ)

A = 2 cm, ω = 100, Φ = π/6.

T = 2π/ω = 2π/100 = π/50 seconds.

For Spring constant,

ω² = k/m

∴ k = ω²m

∴ k = 10/1000 × 100²

k = 100 N/m.

(b). Now, Given Equation,

   x = (2.0 cm)sin[(100 /s)t+π/6]

At t = 0,

  x = 2 × Sin(π/6)

  x = 1 m.

Also, v = AωCos(ωt + Φ)

∴ v = 1.73 m/s.

Also, a = -Aω²Sin(ωt + Φ),

a = 100 m/s².

Hope it helps.