A tolley of mass 3.0kg is connected to two identical spring each of force constant `600Nm^(-1)` as shown in figure. If the trolley is displaced from its equilibrium position by 5.0 cm and released, what is
(a) the period of ensuing oscillation?
(b) the maximum speed of trolley?
(c) How much is the total energy dissipated as heat by the time the trolley comes to rest due to damping forces?

Options

A. `0.5ms^(-1)`
B. `1ms^(-1)`
C. `2ms^(-1)`
D. `3ms^(-1)`

Answer

B

Explanation

In the given figure, two identical springs are connected in parallel
`therefore`The effective spring constant is
`k_("eff")=2k=2xx60Nm^(-1)=1200Nm^(-1)`
Here, amplitude, `A=5cm=0.05m,m=3kg`
Angular frequency of oscillation
`omega=sqrt((k_("eff"))/(m))=sqrt((1200Nm^(-1))/(3kg))=20s^(-1)`
maximum speed, `v_(max)=Aomega=(0.05m)(20s^(-1))=1ms^(-1)`