Question

A spring with a spring constant of 100 N/m is relaxed at the beginning. The spring is then compressed by 0.1 m. An object of 0.01 kg is attached to the compressed spring. If the compressed spring is released, the object will experience simple harmonic motion. What is the maximum possible speed of the object during the oscillation

Answer 1

Answer:

Velocity, v = 10 m/s

Explanation:

Spring constant of the spring, k = 100 N/m

Compression in the string, x = 0.1 m

Mass of the spring, m = 0.01 kg

Let v is the maximum possible speed of the object during the oscillation. It can be calculated by equating potential energy stored in the spring and the kinetic energy imparted to the object as :

$\dfrac{1}{2}kx^2=\dfrac{1}{2}mv^2$

$v=\sqrt{\dfrac{kx^2}{m}}$

$v=\sqrt{\dfrac{100\times (0.1)^2}{0.01}}$

v = 10 m/s

So, the maximum possible speed of the object during the oscillation is 10 m/s. Hence, this is the required solution.