Respuesta :
The ideas utilized in this issue are the frequency of simple harmonic motion, Hooke's law, and Newton's second law of motion. First, apply Hooke's law and Newton's second law of motion to determine the spring constant. Utilizing the frequency in terms of the spring constant, determine the frequency.
Newton's second law of motion
Newton's second law of motion states that "the net force acting on an object is equal to the product of that object's mass and its rate of acceleration."
The expression of net force is: -
F = ma
Here,
m = mass
a = acceleration
Hooke’s Law
"The force required to compress or extend the spring is precisely proportionate to the displacement distance," according to Hooke's law.
The magnitude of spring force is: -
F = kx
Where,
k = spring constant
x = displacement
Frequency of SHM: -
The simple harmonic motion is a periodic motion whose expression for frequency is:
f = 1/2π (k / m)0.5
STEP 1. The spring exerts a force on a driver:
f = kx
f = k (0.005m) -------------- (i)
According to Newton’s Law:
F = ma
F = mg
F = 68 * 9.8
F = 666.4N --------------- (ii)
From (i) and (ii)
k (0.005) = 666.4
k = 133280 N/m
The car is suspended vertically from the spring in this instance, as explained. Gravitational acceleration is hence the acceleration that causes the motion.
N/m is the spring constant's SI unit.
STEP 2. The expression for frequency is:
f = 1/2π (k / m)0.5 ----------------- (iii)
Here,
m = total mass (1500+68 = 1568Kg)
k = 133280 N/m
Putting these values in eq. (iii)
f = 1.467 Hz = 1.5 Hz
To learn more about Newton's second law of motion
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