If the total energy of a simple harmonic oscillator is 50 J and the mass is 2 kg

If the total energy of a simple harmonic oscillator is 50 J and the mass is 2 kg, what is the maximum speed of the mass?

If the total energy of a simple harmonic oscillator is 50 J and the mass is 2 kg, what is the maximum speed of the mass?

Step 1: Identify the total energy (E) of the simple harmonic oscillator, which is given as 50 J.
Step 2: Identify the mass (m) of the oscillator, which is given as 2 kg.
Step 3: Use the formula for total energy in a simple harmonic oscillator: E = (1/2)m(v_max)^2.
Step 4: Rearrange the formula to solve for maximum speed (v_max): v_max = sqrt(2E/m).
Step 5: Substitute the values of E and m into the formula: v_max = sqrt(2*50/2).
Step 6: Calculate the value inside the square root: 2*50 = 100 and 100/2 = 50.
Step 7: Find the square root of 50: v_max = sqrt(50).
Step 8: Calculate the square root of 50, which is approximately 7.07 m/s.

Simple Harmonic Motion – The question tests understanding of the relationship between total energy, mass, and maximum speed in a simple harmonic oscillator.
Energy Conservation – It assesses the ability to apply the principle of conservation of energy in a mechanical system.
Kinematics – The question involves kinematic equations to derive maximum speed from energy.