Question

Two masses, A and B, are attached to different springs. Mass A vibrates with an amplitude of 8 cm at a frequency of 10 Hz and mass B vibrates with an amplitude of 5 cm at a frequency of 16 Hz. How does the maximum speed of A compare to the maximum speed of B

Answer 1

To solve this problem we will apply the concepts of speed given the simple harmonic movement, for which it defines this speed as

$v_{max} = \omega A$

Here

$\omega =$Angular velocity

A = Amplitude

Recall that the angular velocity is equivalent in terms of the frequency at

$\omega = 2\pi f$

If we replace the value we will have then

$v_{max} = 2\pi f A$

For mass A

$v_{max,A} = 2\pi (10)(0.08) = 5.024m/s$

For mass B

$v_{max.B} = 2\pi (16)(0.05) = 5.024m/s$

Therefore they are equal.