Question

Graph shows the x(t) curves for three experiments involving a particular spring-block system oscillating in SHM. The kinetic energy of the system is maximum at t = 4 s for the experiment: (Which experiment has highest kinetic energy at given time instant when compared )

• A. 1
• B. 2
• C. 3
• D. All have same kinetic energy

Answer 1

Answer: (B)

2

Answer 2

At t=4 s, the displacement x=0 for all three experiments. In SHM, kinetic energy is maximum when displacement is zero. Thus, at t=4 s, the kinetic energy of each system is equal to its total energy. The total energy of a spring-block system is $E = \frac{1}{2}kA^2$. Since $k$ is the same for all experiments, the experiment with the largest amplitude has the highest kinetic energy. Experiment 2 has the largest amplitude. Alternatively, comparing the speeds at t=4s: $|v_1(4)| = A\frac{\pi}{8}$, $|v_2(4)| = A\frac{\pi}{4}$, $|v_3(4)| = A\frac{\pi}{8}$. Since $|v_2(4)|$ is the greatest, experiment 2 has the highest kinetic energy.