Question

Objects of equal mass are oscillating up and down in simple harmonic motion on two different vertical springs. The spring constant of spring 1 is 155 N/m. The motion of the object on spring 1 has twice the amplitude as the motion of the object on spring 2. The magnitude of the maximum velocity is the same in each case. Find the spring constant of spring 2.

Answer 1

Maximum velocity = w * (amplitude)

w is the angular frequency sqrt (k/m)

If the maximum velocities are the same, and object 1 has twice the amplitude, then its angular frequency must be half that of object 2. The natural frequency of object 2 is twice that of object 1.

Since the masses are equal, k is 4 times higher for object 2, or 620 N/m