A simple harmonic oscillator has a total energy of 50 J and an amplitude of 10 c

A simple harmonic oscillator has a total energy of 50 J and an amplitude of 10 cm. What is the spring constant?

A simple harmonic oscillator has a total energy of 50 J and an amplitude of 10 cm. What is the spring constant?

Correct Answer: 500 N/m

Step 1: Understand that the total energy (E) of a simple harmonic oscillator is given by the formula E = (1/2)kA^2, where k is the spring constant and A is the amplitude.
Step 2: Identify the values given in the problem. The total energy E is 50 J and the amplitude A is 10 cm. Convert the amplitude from cm to meters: 10 cm = 0.1 m.
Step 3: Substitute the known values into the formula: 50 = (1/2)k(0.1^2).
Step 4: Calculate (0.1^2), which is 0.01.
Step 5: Rewrite the equation with the calculated value: 50 = (1/2)k(0.01).
Step 6: Multiply both sides of the equation by 2 to eliminate the fraction: 100 = k(0.01).
Step 7: Divide both sides by 0.01 to solve for k: k = 100 / 0.01.
Step 8: Calculate the value of k: k = 10000 N/m.

Simple Harmonic Motion – The behavior of oscillating systems where the restoring force is proportional to the displacement from equilibrium.
Energy in Simple Harmonic Oscillator – The total mechanical energy in a simple harmonic oscillator is constant and is given by the formula E = (1/2)kA^2, where k is the spring constant and A is the amplitude.
Spring Constant – A measure of the stiffness of a spring, defined as the force required to compress or extend the spring by a unit distance.