Question

Column 1 Column 2
a) A linear S.H.M e) $\frac{d^2\Theta }{d{t}^2}=\frac{c}{\Theta }$
b) Angular S.H.M f)$\frac{d^{2}x}{d{t}^2}+\frac{R}{m}\frac{dx}{Mt}+x{w}^2=\frac{F}{m}cos\theta$
c) Damped harmonic

motion g) $\frac{d^{2}x}{d{t}^2}-\frac{k}{m}x=0$
d) forced oscillation h) $m\frac{d^{2}x}{d{t}^2}+R\frac{dn}{dt}+mx{\omega }^2=0$

• A. a-e, b-h, c-g, d-f
• B. a-f, b-g, c-e, d-h
• C. a-g, b-e, c-h, d-f
• D. a-g, b-h, c-e, d-f

Answer 1

Answer: (C)

a-g, b-e, c-h, d-f

Differential equation of a linear SHM is given by $\frac{d^{2}x}{d{t}^2}+\frac{k}{m}x=0$

Differential equation of a angular SHM is given by $\frac{d^2\Theta }{d{t}^2}+\frac{\kappa \Theta }{I}=0$

Differential equation of a forced oscillation is given by $\frac{d^{2}x}{d{t}^2}+\frac{R}{m}\frac{dx}{Mt}+x{\omega }^2=\frac{F}{m}cos\theta$
Differential equation of a damped harmonic motion is given by $\frac{d^{2}x}{d{t}^2}+\frac{R}{m}\frac{dx}{Mt}+x{\omega }^2=0$
so the correct matching set is {a-g, b-e, c-h, d-f};