Question

Which of the following combinations of mass and spring constant will give a spring-mass system with the same period as a $1.0m$ long pendulum on earth?

• A. Mass - Spring Constant, $10kg=10N/m$
• B. Mass - Spring Constant, $10kg=1N/m$
• C. Mass - Spring Constant, $20kg=10N/m$
• D. Mass - Spring Constant, $1kg=2N/m$
• E. Mass - Spring Constant, $1kg=10N/m$

Answer 1

The correct option is E Mass - Spring Constant, $1kg=10N/m$

Time period of pendulum $T_p=2\pi \sqrt{\frac{l}{g}}$

Time period of spring-mass system $T_s=2\pi \sqrt{\frac{M}{k}}$

$\therefore$ $T_s=T_p$ $⟹\frac{M}{k}=\frac{l}{g}$

OR $\frac{M}{k}=\frac{1.0}{10}=0.1$

Hence option E is correct.