What will be the amplitude and frequency of vibration

The frequency and period of the resulting motion will depend on the spring constant and mass of the object. In summary, a fisherman's scale with a spring constant of 1295 N/m stretches 2.8 cm when a 3.7 kg fish hangs from it. When the fish is pulled down an additional 2.5 cm and released, it will vibrate with an amplitude of 2.5 cm and a frequency of 2.976 Hz.
  • #1
199
0
A fisherman’s scale stretches 2.8 cm when a 3.7 kg fish hangs from it.
a. What is the spring constant, and
b. What will be the amplitude and frequency of vibration of the fish is pulled down 2.5 cm more and released so that it vibrates up and down?
a)
F=ma
F=(3.7 kg)( 9.8 N/kg)=36.26 N

F = -kx
36.26 N=-k(- 0.028 m)
k=1295 N/m

b)
k=1295 N/m
m=3.7 kg
T = 2pi sqrt(m/k)= 2p sqrt(3.7 kg/1295 N/m)= 0.336 s

F = 1/T=1/(0.336 s)=2.976 Hz

The amplitude would be 2.5 cm more.

Would this amplitude be correct say for the problem??
 
Physics news on Phys.org
  • #2
I think you have it. I'm not sure what you are asking. When an oscillator is displaced and released from rest, the amplitude is the intitial displacement from equilibrium.
 
  • #3
Yes, the amplitude would be correct for the given problem. However, it is important to note that the amplitude of a vibration can change depending on the external forces acting on the system. In this scenario, the amplitude would remain constant as long as the fish is not disturbed by any external forces.
 

1. What factors affect the amplitude and frequency of vibration?

The amplitude and frequency of vibration are affected by several factors, including the mass and stiffness of the vibrating object, the type of material the object is made of, and the amount of energy input into the system.

2. How are amplitude and frequency related in a vibrating system?

Amplitude and frequency are inversely proportional in a vibrating system. This means that as the frequency increases, the amplitude decreases and vice versa.

3. How is the amplitude and frequency of vibration measured?

The amplitude of vibration is usually measured in units of displacement, such as meters or millimeters. The frequency of vibration is measured in units of cycles per second, or hertz (Hz).

4. What is resonance and how does it affect the amplitude and frequency of vibration?

Resonance is a phenomenon that occurs when an object is subjected to an external force that matches its natural frequency of vibration. This results in a significant increase in the amplitude of vibration, while the frequency remains the same.

5. Can the amplitude and frequency of vibration be controlled?

Yes, the amplitude and frequency of vibration can be controlled by adjusting the factors that affect them, such as the mass, stiffness, and energy input into the system. This can also be achieved by using damping techniques to reduce the amplitude and change the frequency of vibration.

Suggested for: What will be the amplitude and frequency of vibration

Back
Top