Question

Graph shows the $x\left(t\right)$ curves for three experiments involving a particular spring - block system executing SHM.
Which of the following situations shown in the graph, has the highest value of maximum kinetic energy of the system at $t=4\text{sec}$.

• A. $1$
• B. $2$
• C. $3$
• D. Same in all

Answer 1

The correct option is A $1$

Given that, Kinetic energy is maximum at $t=4\text{s}$, Where $x=0.$
We know that, Kinetic energy of a particle at mean position is given by
$K=\frac{1}{2}m{\omega }^2{A}^2.....\left(i\right)$
From the figure, we can deduce that $3$ is not a correct option, as the particle is at the extreme position, where kinetic energy should be a minimum.

It is evident from the figure that, Amplitude of $1$ is more than the Amplitude of $2$ and curves $1\&2$ have same angular frequency.
Hence, both represent the equation $x=A\cos \omega t$.

$\therefore$ From $\left(i\right)$ we can say that, Kinetic energy of the system is maximum at $t=4\text{s}$ for curve $1$
Thus, option (a) is the correct answer.