Answer:
Total mechanical energy in the system, E = 36 J
Explanation:
It is given that,
Mass of the object, m = 2 kg
It undergoes undamped simple harmonic motion, with a position given by :
[tex]x(t)=2\ cos(3t+\pi)[/tex]
The general equation of SMH is given by :
[tex]x(t)=A\ cos(\omega t+\pi)[/tex]
A is the amplitude of wave, A = 2 m
[tex]\omega=3[/tex] is the angular frequency
We know that the sum of kinetic and potential energy is equal to the mechanical or total energy of the system. The formula for the mechanical energy is given by :
[tex]E=\dfrac{1}{2}m\omega^2A^2[/tex]
So,
[tex]E=\dfrac{1}{2}\times 2\times (3)^2\times 2^2[/tex]
E = 36 joules
So, the total mechanical energy in the system is 36 joules. Hence, this is the required solution.
