Two masses A & B each of 5 kg are suspended by a light inextensible st...
And B are connected by a spring. Mass A has a mass of 2 kg and is attached to the spring, while mass B has a mass of 3 kg and is free to move. The spring has a spring constant of 5 N/m.
a) Calculate the natural frequency of the system.
The natural frequency of the system can be calculated using the formula:
f = 1/(2π) * √(k/m)
where f is the natural frequency, k is the spring constant, and m is the equivalent mass of the system.
The equivalent mass of the system can be calculated as:
m = m1 + m2
where m1 is the mass of mass A and m2 is the mass of mass B.
m = 2 kg + 3 kg = 5 kg
Substituting the values in the formula:
f = 1/(2π) * √(5 N/m / 5 kg)
f = 1/(2π) * √(1)
f = 0.159 Hz
Therefore, the natural frequency of the system is 0.159 Hz.
b) If mass B is displaced by 0.1 m from its equilibrium position and released, calculate the maximum displacement of mass B.
The maximum displacement of mass B can be calculated using the formula:
x = A * cos(2πft)
where x is the displacement of mass B, A is the amplitude of the motion, f is the natural frequency, and t is time.
The amplitude of the motion can be calculated as:
A = x0
where x0 is the initial displacement of mass B.
A = 0.1 m
Substituting the values in the formula:
x = 0.1 cos(2π * 0.159 t)
The maximum displacement occurs when cos(2πft) = 1, which happens at t = 0.
Therefore, the maximum displacement of mass B is:
x = 0.1 cos(0)
x = 0.1 m
Therefore, the maximum displacement of mass B is 0.1 m.
Two masses A & B each of 5 kg are suspended by a light inextensible st...
As A is on table so there must be book change in height if u move B. more accurate answer can be given if diagram was available
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