# How do you convert ordinary frequency to angular frequency?

• michaeltozer13
In summary, to find the oscillation frequency of a 22 kg block oscillating back and forth on a frictionless horizontal surface, we can use the equation angular frequency=sqrt(k/m) and period=2pisqrt(m/k). The amplitude of the oscillation is 22.0 cm (0.22m), the angular frequency is 25.0 rad/s, and the phase angle is pi. To convert ordinary frequency (f) in cycles/sec to angular frequency (w) in radians/sec, we need to multiply f by 2pi.
michaeltozer13

## Homework Statement

A 22 kg block oscillates back and forth along a straight line on a frictionless horizontal surface. Find the oscillation frequency, if its displacement from the origin is given by

x(t) = (22.0 cm)·cos((25.0 rad/s)t + π).

## Homework Equations

angular frequency=sqrt(k/m)
period=2pisqrt(m/k)
period=1/frequency

## The Attempt at a Solution

okay so from the equation they gave us i think the 22.0 cm (0.22m) is the amplitude of the oscillation, and 25.0 rad/s is the angular frequency, and the pi is the is the phase angle. So I am trying to solve for oscillation frequency but I am not sure how to start the problem. Any solid help with trying to start this problem would be appreciated, Thanks!

How is angular frequency related to frequency of the oscillation?

Im honestly not sure how they are related, i feel like that is part of the reason why I am lost when it comes to this question. Any help on trying to understand there relationship?

Angular frequency tells you how many radians per second. How many radians are there in one complete oscillation?

There is 2pi radians in one oscillation isn't there?

michaeltozer13 said:
There is 2pi radians in one oscillation isn't there?
Exactly. So to convert ordinary frequency (##f##) in cycles/sec to angular frequency (##\omega##) in radians/sec, what would you have to do?

## 1. What is the equation for a spring and mass system?

The equation for a spring and mass system is F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the mass from its equilibrium position.

## 2. How does the mass affect the period of oscillation in a spring and mass system?

The period of oscillation in a spring and mass system is not affected by the mass. It only depends on the stiffness of the spring and the force applied to the system.

## 3. What is the difference between a simple harmonic motion and a damped harmonic motion?

A simple harmonic motion is a periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction. A damped harmonic motion is a periodic motion where the amplitude decreases over time due to an external force, such as friction or air resistance.

## 4. How does the spring constant affect the period of oscillation in a spring and mass system?

The period of oscillation in a spring and mass system is inversely proportional to the square root of the spring constant. This means that a higher spring constant will result in a shorter period of oscillation.

## 5. Can the spring and mass system be used to model real-world systems?

Yes, the spring and mass system can be used to model various real-world systems, such as a car's suspension system or a bungee jumper's motion. It is a useful tool for understanding and predicting the behavior of many physical systems.

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