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Question: The equation of motion of a particle is \(\frac { d ^ { 2 } y } { d t ^ { 2 } } + k y = 0\)where *k*...

The equation of motion of a particle is d2ydt2+ky=0\frac { d ^ { 2 } y } { d t ^ { 2 } } + k y = 0where k is a positive constant. The time period of the motion is given by

A

2πk\frac { 2 \pi } { k }

B

2πk2 \pi k

C

2πk\frac { 2 \pi } { \sqrt { k } }

D

2πk2 \pi \sqrt { k }

Answer

2πk\frac { 2 \pi } { \sqrt { k } }

Explanation

Solution

Standard equation md2ydt2+ky=0m \frac { d ^ { 2 } y } { d t ^ { 2 } } + k y = 0and in a given equation m =1 and k = k

So, =2πk= \frac { 2 \pi } { \sqrt { k } }