Two springs with negligible masses and force constants `k_1=200(N)/(m)` and `K_2=160(N)/(m)` are attached to the block of mass `m=10kg ` as shown in the fig. Initially the block is at rest, at the equilibrium position which both springs are neither stretched nor compressed. At time `t=0`, sharp impulse of `50Ns` is given to the block with a hammer along the spring.

Options

A. Period of oscillations for the mass m is `(pi)/(6)`s.
B. Maximum velocity of the mass m during its oscillation is `10(m)/(s)`
C. Data are insufficient to determine maximum velocity.
D. Amplitude of oscillation is `0.83m`.

Answer

D

Explanation

`T=2pisqrt((m)/(K_1+K_2))=2pisqrt((10)/(360))=(pi)/(3)s`
the maximum velocity is always at equilibrium position since at any other point there will be a restoring force at temting to slow the mass.
`V_("mass")=("impulse")/("mass")=(50)/(10)=5(m)/(s)impliesomega=(2pi)/(T)=6(rad)/(s)`
`impliesA=`amplitude`=(V_(max))/(omega)=(5)/(6)=0.83m`