Auniform beam is suspended horizontally by two identical vertical springs that are attached between the ceiling and each end of the beam. the beam has mass 225 kg, and a 175-kg sack of gravel sits on the middle of it. the beam is oscillating in shm, with an amplitude of 40.0 cm and a frequency of 0.600cycles/s. part a the sack of gravel falls off the beam when the beam has its maximum upward displacement. what is the frequency of the subsequent shm of the beam?

The frequency as calculated is 0.79 Hz

Solution:

As per the question:

Mass of the beam, m = 225 kg

Mass of the sack, m' = 175 kg

Amplitude, A = 40.0 cm = 0.4 m

Frequency, f = 0.6 Hz

Now,

(A) To calculate the frequency of the SHM:

The total mass, M = m + m' = 225 + 175 = 400 kg

With the help of the eqn:

where

k = spring constant

Thus

Squaring both sides, we get:

k = 5684.89 N/m

Now, after the gravel has fallen:

m = 275 kg

Now,

The frequency of the SHM can be calculated as:

not too sure thinking all accelerations are pointed down