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 150 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

Solution)

Given,

Spring constant, k1 = 150 N/m

Also,

Amplitude, A1 = 2 A2

Maximum velocity and masses are same in both cases, hence maximum kinetic energies are also same in both cases .

Total energy, E of both oscillators will also be same.

So, E = (1/2)k1(A1)^2 =(1/2)k2(A2)^2

k1(2A2)^2 =k2(A2)^2

k2 = 4 k1 =4*150= 600 N/m

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