# Periodic Time Calculation for Simple Harmonic Motion with a Spring

• Ch3m_
In summary, Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium and is always directed towards the equilibrium position. The Periodic Time for SHM with a spring is calculated using the formula T = 2π√(m/k), where T is the period in seconds, m is the mass of the object attached to the spring in kilograms, and k is the spring constant in newtons per meter. The Periodic Time is an important parameter as it determines the frequency of the motion and is affected by the mass and spring constant. Real-life examples of SHM with a spring include a weight attached to a spring, a door being opened and closed, a
Ch3m_

## Homework Statement

A 0.61 kg mass attached to a spring (k = 27 N m-1) is performing SHM on a smooth horizontal surface.
Calculate the periodic time of these oscillations.

ω=2π/T
ω=2πƒ

## The Attempt at a Solution

I think I need to find out the angular frequency ω of the oscillations in order to calculate the periodic time using ω=2π/T, but I have no idea how to calculate ω since it doesn't give you the frequency ƒ ?

Ch3m_ said:
I have no idea how to calculate ω since it doesn't give you the frequency ƒ ?
Check your textbook for the relationship between frequency, mass, and spring constant.

Ch3m_

## What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement from equilibrium and is always directed towards the equilibrium position. This results in a sinusoidal motion.

## How is the Periodic Time Calculated for Simple Harmonic Motion with a Spring?

The Periodic Time for Simple Harmonic Motion with a Spring is calculated using the formula T = 2π√(m/k), where T is the period in seconds, m is the mass of the object attached to the spring in kilograms, and k is the spring constant in newtons per meter.

## What is the significance of the Periodic Time in Simple Harmonic Motion?

The Periodic Time in Simple Harmonic Motion is the time it takes for one complete cycle of the motion. It is an important parameter as it determines the frequency of the motion, which is directly related to the energy and amplitude of the oscillation.

## How does the mass and spring constant affect the Periodic Time in Simple Harmonic Motion?

As the mass increases, the Periodic Time also increases, meaning that the oscillation takes longer to complete one cycle. Similarly, as the spring constant increases, the Periodic Time decreases, resulting in a faster oscillation.

## What are some real-life examples of Simple Harmonic Motion with a Spring?

Some examples of Simple Harmonic Motion with a Spring include a weight attached to a spring, a door being opened and closed, a pendulum, and a mass-spring system in a car's suspension system.

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