Question

The equation of a SHM of amplitude $a$ and angular frequency $\omega$ in which all distances are measured from one extreme position and time is taken to be zero at the other extreme position is

• A. $x=a\sin \omega t$
• B. $x=a\cos \omega t$
• C. $x=a-a\sin \omega t$
• D. $x=a+a\cos \omega t$

Answer 1

Answer: (D)

If SHM. starts from means position, then
$x_0=a\sin \left(\omega t+{\theta }_0\right)$
Now, $x=x_0-(-a)\Rightarrow x=x_0+a=a+a\sin \left(\omega +{\theta }_0\right)$
At $t=0,x=2a$
$\Rightarrow 2a=a+a\sin \left(\omega (0)+{\theta }_0\right)$
$\Rightarrow {\theta }_0=\frac{\pi }{2}$ or $x=a+a\sin \left(\omega t+\frac{\pi }{2}\right)$
$\Rightarrow x=a+a\cos \omega t$