Question

Two springs with negligible masses and force constants $k_1=200N/m$ and $k_2=160N/m$ are attached to the block of mass $m=10kg$ as shown in the figure. Initially the block is at rest, at the equilibrium position in which both springs are neither stretched nor compressed. At time $t=0s$, sharp impulse of $50Ns$ is given to the block with a hammer along the spring.

• A. Period of oscillations for the mass m is $\frac{\pi }{6}s$
• B. Maximum velocity of the mass m during its oscillation is $10m/s$
• C. Data are insufficient to determine maximum velocity
• D. Amplitude of oscillation is $0.83m$.

Answer 1

The correct option is D Amplitude of oscillation is $0.83m$.

We know that,
$T=2\pi \sqrt{\frac{m}{K_1+K_2}}=2\pi \sqrt{\frac{10}{360}}=\frac{\pi }{3}s$

The maximum velocity is always at equilibrium position since at any other point, there will be a restoring force tending to slow the mass.

$V_{max}=\frac{impulse}{mass}=\frac{50}{10}=5m/s$

$\omega =\frac{2\pi }{T}=6rad/s$

$A=$amplitude
$=\frac{V_{max}}{\omega }=\frac{5}{6}=0.83m$