Question

a body oscillates with shm according to the equation x(t) = 10cos (2pie t+ pie by 6) where x is in metre and t is in second

calculate
(1) displacement at time t =0
(2) magnitude of maximum velocity
(3) angular displacement ​

Answer 1

JunaidMirza Physics Newton

(1)

x = 5 cos(2πt + π/4)

At t = 1.5 s

x = 5 cos[(2π × 1.5) + π/4]

x = 5 cos (13π/4)

x = -3.53 m

(2)

v = A ω cos (ωt + φ)

= 5 × (2 π) cos [(2 π × 1.5) + π/4]

[∵ by comparing given equation and general SHM equation ω = 2 π]

= 31.4 × 0.99

= 31.35 m/s

(3)

Acceleration = -A ω² sin(ωt + φ)

= -5 × (2 π)² sin[(2 π × 1.5) + π/4]

= -0.283 rad/s^2

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