The equation of motion of a particle executing SHM is, α +16π 2x=0. In this equation α is the linear acceleration in m/s2, of the particle at a displacement x metre. The time period of SHM, in second, is:

Question

The equation of motion of a particle executing SHM is, α +16π 2x=0. In this equation α is the linear acceleration in m/s2, of the particle at a displacement x metre. The time period of SHM, in second, is: (A)  (1/4)  (B)  (1/2)  (C) 1 (D) 2

Tardigrade Admin · Accepted Answer

The equation of motion and particles executing SHM is given by α +16π 2x=0 α =-16π 2x But from the relation in SHM, acceleration is given by α =-ω 2x So, -ω 2x=-16π 2x or ω =4π (∵ ω =2(π /T)) or (2π /T)=4π Hence, T=(1/2)s

Q. The equation of motion of a particle executing SHM is, $α + 16 π^{2} x = 0.$ In this equation $α$ is the linear acceleration in $m / s^{2},$ of the particle at a displacement x metre. The time period of SHM, in second, is:

$\frac{1}{4}$

$\frac{1}{2}$

1

2

Q. The equation of motion of a particle executing SHM is, α+16π2x=0. In this equation α is the linear acceleration in m/s2, of the particle at a displacement x metre. The time period of SHM, in second, is:

41​

21​

1

2

The equation of motion and particles executing SHM is given by α+16π2x=0 α=−16π2x But from the relation in SHM, acceleration is given by α=−ω2x So, −ω2x=−16π2x or ω=4π (∵ω=2Tπ​) or T2π​=4π Hence, T=21​s

Q. The equation of motion of a particle executing SHM is, $α + 16 π^{2} x = 0.$ In this equation $α$ is the linear acceleration in $m / s^{2},$ of the particle at a displacement x metre. The time period of SHM, in second, is:

$\frac{1}{4}$

$\frac{1}{2}$