An object performs SHM of amplitude 5 cm and time period 4 s. If timing is started when the object is at the centre of the oscillation i.e., x=0 then calculate.
(i) Frequency of oscillation.
(ii) The displacement at 0.5 S.

Explanation

(i) Frequency `f = (1)/(T) = (1)/(4) = 0.25 Hz`
(ii) The displacement equation of object `x = Asinomegat` at `t = 0.5` s,
`x = 5sin(2pi xx 0.25 xx 0.5) = 5sin"(pi)/(4) = (pi)/(sqrt(2)) cm`
(iii) Maximum accleration `a_("max") = omega^(2)A = (0.5 pi)^(2) xx 5 = 12.3 cm//s^(2)`
(iv) Velocity at `x = 3 cm` is `v = +- omegasqrt(A^(2) - x^(2)) = +- 0.5pisqrt(5^(2)-3^(2)) = +- 6.28 cm//s`