The displacement of a certain suspended object is found to satisfy the differential…

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

The displacement

x

of a certain suspended object is found to satisfy the differential equation

\displaystyle \frac{d^{2}x}{dt^{2}}+4.9\,x=0

. Assume small oscillations and

g=9.8\,\text{m\,s}^{-2}

. (i) Compare the given equation with the standard form of simple harmonic motion and write down the angular frequency

\omega

. (ii) Determine the effective length

L

of the corresponding simple pendulum. (iii) Calculate the time period

T

of the oscillations.