A 5 kg collar is attached to a spring of spring constant 500 N `m^(-1)`. It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by 10.0 cm and released. Calculate
(a) the period of oscillation,
(b) the maximum speed and
(c) maximum acceleration of the collar.

Explanation

Spring constant `k= 500 Nm^(-1)`
Mass of collar `m = 5kg`
Amplitude `A = 10 cm = 0.1 m`
The velocity of collar executing SHM is, `v(t) = A omega sin (omega t+phi)` and for maximum speed `sin (omega t+phi)= -1`
`therefore v_("max") = A omega`
`=A xx sqrt((k)/(m)) = 0.1xx sqrt((500)/(5)) = 0.1 xx sqrt(100)`
`v_("max") = ms^(-1)` and it occur at x=0.