Question

A particle attached to a spring executes
simple harmonic motion. If the total
energy of the same particle
the same particle is doubled then its time period? ​

Answer 1

Answer:

Okay, when the velocity is a max, all the energy of the system will be kinetic energy. This is because the max velocity occurs at x = 0, where x is the extension of the spring. As there is no extension of the spring, the energy stored in the spring is also zero.

The kinetic energy of the spring will be equal to 5.16 J, subbing in 0.323 (323 g in kg) for the mass, you can solve for the velocity. This gives v = 5.65 m/s

To find the spring constant, use the equation omega = 2pi/T, where T is the period, and omega is the angular velocity. Subbing 0.22 s for T and solving for omega gives 28.56 rad/s. Then using the equation v = r*omega, subbing in v = 5.65 m/s and omega = 28.56 rad/s, you get r = 0.20 m.

The radius calculated is your amplitude of motion. Using this you can calculate the force constant in the spring.  

When the spring is at max extension, the velocity is zero and therefore kinetic energy of the system is zero. The extension of the spring (x) is the same as the amplitude of motion and can be used to calculate the force constant, using the equation E = 1/2kx^2. Setting E = 5.16 J and x = 0.20, solving this for k gives, k = 258 N/m

Explanation: