A 5 kg collar is attached to a spring of spring constant 500`Nm^(-1)` . It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by 10 cm and released. Calculate (a) The period of oscillations (b) The maximum speed and (c) maximum acceleration of the collar.

Explanation

Here, `m=5kg, k=500Nm^(-1)`
`A=10.0cm=0.10m`
(i) Period of oscillation,
`T=2pisqrt((m)/(k))=2xx(22)/(7)sqrt((5)/(500))`
`=2xx(22)/(7)xx(1)/(10)=0.628s`
(ii) The maximum speed, `v_(max)=Aomega =Asqrt((k)/(m))`
`=0.10xxsqrt((500)/(5))=0.1xx10=1.0ms^(-1)`
(iii) The maximum acceleration fo the collar
`a_(max)=omega^(2)A=(k)/(m)A=(500)/(5)xx0.10=10ms^(-2)`