A mass attached to a spring oscillates with a maximum speed of 4 m/s. If the spr

A mass attached to a spring oscillates with a maximum speed of 4 m/s. If the spring constant is 100 N/m, what is the maximum displacement?

A mass attached to a spring oscillates with a maximum speed of 4 m/s. If the spring constant is 100 N/m, what is the maximum displacement?

Step 1: Identify the maximum speed (v_max) given in the problem, which is 4 m/s.
Step 2: Identify the spring constant (k) given in the problem, which is 100 N/m.
Step 3: Use the formula for angular frequency (ω), which is ω = √(k/m).
Step 4: Assume a mass (m) of 1 kg for simplicity, since it is not provided.
Step 5: Calculate ω using the values: ω = √(100 N/m / 1 kg) = √100 = 10 rad/s.
Step 6: Use the relationship between maximum speed and amplitude: v_max = ωA.
Step 7: Rearrange the formula to find amplitude (A): A = v_max / ω.
Step 8: Substitute the values: A = 4 m/s / 10 rad/s = 0.4 m.
Step 9: Conclude that the maximum displacement (amplitude) is 0.4 m.

Simple Harmonic Motion – The relationship between maximum speed, angular frequency, and amplitude in oscillatory motion.
Spring Constant and Mass – Understanding how the spring constant and mass affect the angular frequency of the system.