Question

Which of the following equations can be that of an SHM? Here, x represents displacement from mean position.

t represents time

k is a positive constant

v represents velocity

• A. $\frac{m{d}^{2}x}{d{t}^2}-kx=0$
• B. $\frac{m{d}^{2}x}{d{t}^2}+kx=0$
• C. $\frac{mdv}{dt}+kx=0$
• D. $K{\int }_0^{t}vdt=-m\frac{d^{2}x}{d{t}^2}$ .

Answer 1

Answer: (B), (C), (D)

$K{\int }_0^{t}vdt=-m\frac{d^{2}x}{d{t}^2}$ .

General equation of Linear SHM is kx = -ma (displacement and acceleration will have opposite signs)

Except option (a) all other are the same

$kx=-ma$......(1)

$\Rightarrow kx=-\frac{mdv}{dt}$

$\Rightarrow kx+\frac{mdv}{dt}=0$...... Option(c)

From equation $kx=-\frac{m{d}^{2}x}{d{t}^2}$........ (ii)

$kx=-\frac{m{d}^{2}x}{d{t}^2}$ ...... Option(b)

From $e{q}^n$ (ii) $kx=\frac{-m{d}^{2}x}{d{t}^2}$

$k{\int }_0^{t}vdt=-\frac{m{d}^{2}x}{d{t}^2}$ ...... Option(d)