Question

There is a body having mass m and performing S.H.M. with amplitude a. There is a restoring force $F = - Kx$ , where x is the displacement. The total energy of body depends upon:
A) $K,x$
B) $K,a$
C) $K,a,x$
D) $K,a,v$

Answer 1

Hint:
Here in this question, it is given that there is a body whose mass is m and that body is performing as simple harmonic motion with an amplitude A and a restoring force is also given as from the total conclusion we have to state that the total energy will depend upon which of the terms given in the option section. Here we can use the concept of total energy of SHM.



Formula used :
The total energy of body performing simple harmonic motion is given as,
$U = \dfrac{1}{2}K{a^2}$


Complete step by step solution:
As before starting the solution of this question, we just write all the given things from the question,
Mass of the Body is m,
Amplitude is denoted as a,
Restoring force, $F = - Kx$ , where x is the displacement.
To find the Total energy of the body depends upon,
So, as we know that, the total energy of body performing simple harmonic motion is given as,
$U = \dfrac{1}{2}K{a^2}$
As from the above conclusion as formula we get that, the total energy will depend upon $K,a$ respectively.
Therefore, the correct answer is $K,a$ .
Hence, the correct option is (B).



Hence the correct answer is Option(B).






Note:
As this question is taken from energy in simple harmonic motion so let us discuss what is energy in simple harmonic motion. In a straightforward harmonic oscillator, the energy alternates between the kinetic energy, and the potential energy. Since there are no dissipative forces in the SHM of the mass and spring system, the total energy is the sum of the kinetic and potential energies.