Question

In SHM match the following
Column I Column II
a) Maximum velocity e) 1/2 M${\omega }^2{A}^2$
b) Maximum acceleration f) 1/4 M${\omega }^2{A}^2$
c) Maximum Force g) A$\omega$
d) Maximum total energy h) ${\omega }^{2}A$
i) $m{\omega }^{2}A$

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

Answer 1

The correct option is A a-g, b-h, c-i, d-e

$V_{max}=A\omega$ from substituting $x=0$
$v=\omega \sqrt{A^2-x^2};v=\omega A$
$a_{max}=-{\omega }^{2}x$ where $x$ is replaced by A.
$=-{\omega }^{2}A$
Max. force $=m\times a_{max}$
$=-m{\omega }^{2}A$
Max energy $=\frac{1}{2}m{v_{max}}^2=\frac{1}{2}m{\omega }^2{A}^2$