a mass of 40kg moves under the influence of a spring whose force constant is 14N/m,calculate the frequency of vibration
To calculate the frequency of vibration, you can use Hooke's Law and the formula for the frequency of vibration of a mass-spring system.
Hooke's Law states that the force exerted by a spring is directly proportional to the displacement of the mass from its equilibrium position. It can be expressed as:
F = -kx
Where:
F is the force exerted by the spring,
k is the force constant, and
x is the displacement from the equilibrium position.
In this case, the force constant k is given as 14 N/m. The force exerted by the spring (F) is given by the equation:
F = ma
Where:
m is the mass of the object, and
a is the acceleration of the object.
Since the system is in simple harmonic motion, the acceleration is given by the equation:
a = -ω²x
Where:
ω is the angular frequency (in radians per second).
By combining the equations, we can find the angular frequency (ω):
F = ma
-mkx = m*(-ω²x)
ω² = k/m
The angular frequency (ω) is related to the frequency (f) by the formula:
ω = 2πf
We can substitute ω² into the equation:
ω² = k/m
(2πf)² = k/m
f = √(k/m)/(2π)
Plugging in the given values:
k = 14 N/m
m = 40 kg
f = √(14 N/m)/(40 kg))/(2π)
f = √(0.35 N/(kg⋅m)) / (2π)
f ≈ 0.167 Hz
Therefore, the frequency of vibration is approximately 0.167 Hz.