Question 175: Oscillations

Question

The velocity of a particle executing SHM varies with displacement $(x)$ as $4 v^{2}=50-x^{2}$. The time period of oscillations is $\frac{x}{7} s$. The value of $x$ is ___________. $\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$

Accepted Answer

$$4{v^2} = 50 - {x^2}$$
or $$v = {1 \over 2}\sqrt {50 - {x^2}} $$
Comparing the above equation with $$v = \omega \sqrt {{A^2} - {x^2}} $$
$$ \Rightarrow \omega  = {1 \over 2}$$
& $$A = \sqrt {50} $$
so $${{2\pi } \over T} = {1 \over 2}$$
$$ \Rightarrow T = 4\pi \sec $$
$$ = 4 	imes {{22} \over 7}\sec $$
$$T = {{88} \over 7}\sec $$
so $$x = 88$$

Oscillations

The velocity of a particle executing SHM varies with displacement (x) as 4 v^{2}=50-x^{2}. The time period of oscillations is \frac{x}{7} s. The value of x is ___________. \left(\right. Take \left.\pi=\frac{22}{7}\right)

Integer / Numeric Answer Type