# How Do You Calculate Period and Frequency of a Harmonic Oscillator?

• chocolatelover
In summary, to find the period of a simple harmonic oscillator that completes four vibrations in 11.5 seconds, divide the time by 4. To find the frequency in Hertz, take the inverse of the period. To find the angular frequency in radians per second, divide the frequency by 2pi and multiply by 60 seconds.
chocolatelover
Hi everyone,

## Homework Statement

A simple harmonic oscillator takes 11.5s to undergo four complete vibrations.

a. Find the period of its motion
b. Find the frequency in Hertz
c. Find the angular frequency in radians per second

ω=2pi(f)
ω=spi/T
f=ω/2pi

t=1/f

## The Attempt at a Solution

a. ω=2pi/11.5=.546
f=.546/2pi=.858
t=1/f=1.166

b. f=.858

c. ω=.546

Thank you very much

Nope, doesn't look right.

So in order to go back and forth 4 times, it takes 11.5s, right? Your "period" is how long it takes to do this once.

Secondly, frequency in Hz is f = 1/T

Lastly, your angular frequency is w = (2*pi)/T

Thank you very much

Could you please explain to me how to find one of these? Once I can find one, I can find the others. It seems like there isn't enough information given, because the 11.5 s is not used in any of the equations, right?

Thank you

your period is 11.5s divided by 4, i think

once you'be found your period, do the inverse to get your frequency

divide frequency by 2pi, multiply by 60s to get rad/s

i think i am correct, try it

Thank you very much

Isn't 11.5 just the time or is that also the period?

Thank you

no i think the problems means that it makes 4 cycles in 11.5 seconds, so a period equals the time of one cycle, so in order to find period from the given time, divide time by 4. try it.

did it work out correctly?

Yes, that was correct

Thank you very much

Regards

no worries, glad to help

## 1. What is a harmonic oscillator problem?

A harmonic oscillator problem is a mathematical model that describes the motion of a system that experiences a restoring force proportional to its displacement from equilibrium. It is commonly used in physics and engineering to study simple harmonic motion in systems such as springs, pendulums, and vibrating masses.

## 2. What is the equation for a harmonic oscillator?

The equation for a harmonic oscillator problem is F = -kx, where F is the restoring force, k is the spring constant, and x is the displacement from equilibrium. This equation is derived from Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from equilibrium.

## 3. How is a harmonic oscillator problem solved?

A harmonic oscillator problem can be solved using various mathematical techniques, such as differential equations, trigonometric functions, and complex numbers. The solution depends on the specific system and initial conditions. In general, the solution will involve finding the position, velocity, and acceleration of the system as a function of time.

## 4. What is the role of energy in a harmonic oscillator problem?

The total energy of a harmonic oscillator is constant and is equal to the sum of its kinetic and potential energies. As the system oscillates back and forth, the energy is continuously transferred between kinetic and potential forms, but the total energy remains constant. This relationship is known as the principle of conservation of energy.

## 5. How is the period of a harmonic oscillator determined?

The period of a harmonic oscillator is the time it takes for one complete cycle of motion. It can be calculated using the equation T = 2π√(m/k), where T is the period, m is the mass of the system, and k is the spring constant. This equation shows that the period is directly proportional to the square root of the mass and inversely proportional to the square root of the spring constant.

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