An electronic motor of mass 40kg is mounted on four vertical springs each having a spring constant of `4000 Nm^-1`. The period with which the motor vibrates vertically is

Options

A. 0.314s
B. 3.14s
C. 0.628s
D. 0.157s

Answer

A

Explanation

Spring constant of combination
`k_p=k_1+k_2+k_3+k_4`
`k_p=4k`
`=4 times 4000`
`k_p=16000 Nm^-1`
Time period of combination
`T=2 pisqrt(m/k_p)`
`=2pi sqrt(m/(4k))`
`=2pi sqrt(40/16000)`
`T=0.314s`