Question

A 5 kg collar is attached to a spring constant 500 N m–1. It slides without friction over a horizontal rod. The collar is displaced from its equilibrium position by 10 cm and released. The time period of oscillation is

• A. $\frac { \pi } { 5 }$ s
• B. $\frac { \pi } { 2 }$s
• C. $\pi$ s
• D. 2$\pi$ s

Answer 1

Answer: (A)

$\frac { \pi } { 5 }$ s

Answer 2

Here, $\mathrm { m } = 5 \mathrm {~kg} , \mathrm { k } = 500 \mathrm { Nm } ^ { - 1 }$

Time period of oscillation is

$\mathrm { T } = 2 \pi \sqrt { \frac { \mathrm {~m} } { \mathrm { k } } } = 2 \pi \sqrt { \frac { 5 \mathrm {~kg} } { 500 \mathrm { Nm } ^ { - 1 } } } = \frac { 2 \pi } { 10 } \mathrm {~s} = \frac { \pi } { 5 } \mathrm {~s}$