Simple harmonic motion - vibration frequency

A_0, so plugging this into the equation of motion gives:a = -kA_0Using the value for acceleration amplitude, we can rearrange the equation to solve for the angular frequency omega:omega = sqrt(k/m) = sqrt(a/k)Therefore, the frequency of vibration can be calculated using only the acceleration amplitude and the vibration amplitude. This can be useful in situations where the period of oscillations is unknown. In summary, the frequency of sinusoidal vibrations in simple harmonic motion can be calculated using the equation of motion and the values for acceleration amplitude and vibration amplitude.
  • #1
Bugsy23
25
0
I need to calculate the frequency of sinusoidal vibrations in simple harmonic motion. The only known values that I have are the acceleration amplitude and the vibration amplitude. Is there a way of calculating the frequency of vibration without knowing the period of the oscillations?
 
Physics news on Phys.org
  • #2
Bugsy23 said:
I need to calculate the frequency of sinusoidal vibrations in simple harmonic motion. The only known values that I have are the acceleration amplitude and the vibration amplitude. Is there a way of calculating the frequency of vibration without knowing the period of the oscillations?
The equation of motion is:

[tex]F = ma = m\ddot{x} = -kx[/tex]

The general solution is:

[tex]x = A_0\sin(\omega t + \phi)[/tex] where [itex]\omega^2 = k/m[/tex]

[itex]A_0[/itex] is the maximum amplitude of vibration (maximum x). The maximum acceleration occurs when x = ? What is the acceleration at that point? (hint: use the equation of motion to find maximum value for a).

From that you should be able to determine [itex]\omega[/itex]

AM
 
Last edited:

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object moves back and forth in a straight line with a constant amplitude and a fixed period. This type of motion is commonly seen in pendulums, springs, and other vibrating systems.

2. What is the formula for calculating vibration frequency in simple harmonic motion?

The formula for calculating vibration frequency in simple harmonic motion is f = 1/T, where f is the frequency in hertz (Hz) and T is the period in seconds (s).

3. How does the mass affect the vibration frequency in simple harmonic motion?

In simple harmonic motion, the mass of the object does not affect the vibration frequency. The frequency only depends on the stiffness of the spring or restoring force and the mass of the object does not change the stiffness of the spring.

4. Can the amplitude affect the vibration frequency in simple harmonic motion?

No, the amplitude does not affect the vibration frequency in simple harmonic motion. The frequency is only dependent on the stiffness of the system and the mass of the object, not the amplitude of the motion.

5. How can simple harmonic motion be applied in real-life situations?

Simple harmonic motion is seen in many real-life situations, such as the motion of a swing, the vibration of a guitar string, or the motion of a car's suspension system. It is also used in various scientific instruments, such as seismographs to measure earthquakes or in clocks to keep time.

Similar threads

Replies
1
Views
378
Replies
13
Views
264
Replies
8
Views
1K
Replies
21
Views
1K
Replies
7
Views
580
Replies
4
Views
1K
  • Mechanics
Replies
5
Views
9K
Back
Top