A spring of spring constant 30.0 N/m is attached to different masses, and the
system is set in motion. Find the period and frequency of vibration for masses of
the following magnitudes:
a. 2.3 kg
b. 15 g
c. 1.9 kg
To find the period and frequency of vibration for each mass, we can use the formula for the period of a mass-spring system:
T = 2π * √(m/k)
where T is the period, m is the mass, and k is the spring constant.
a. For a mass of 2.3 kg:
T = 2π * √(2.3 / 30)
T = 2π * √(0.077)
T = 2π * 0.278
T = 1.75 s
Frequency, f = 1 / T
f = 1 / 1.75
f = 0.571 Hz
b. For a mass of 15 g (0.015 kg):
T = 2π * √(0.015 / 30)
T = 2π * √(0.0005)
T = 2π * 0.0224
T = 0.140 s
Frequency, f = 1 / T
f = 1 / 0.140
f = 7.14 Hz
c. For a mass of 1.9 kg:
T = 2π * √(1.9 / 30)
T = 2π * √(0.0633)
T = 2π * 0.2517
T = 1.58 s
Frequency, f = 1 / T
f = 1 / 1.58
f = 0.632 Hz
So, the periods and frequencies of vibration for masses of 2.3 kg, 15 g, and 1.9 kg are as follows:
a. T = 1.75 s, f = 0.571 Hz
b. T = 0.140 s, f = 7.14 Hz
c. T = 1.58 s, f = 0.632 Hz