# Simple Harmonic Motion Calculator

The free online Simple Harmonic Motion Calculator will calculate the oscillating object's acceleration, velocity, and displacement in fractions of seconds. To receive the result quickly, enter the amplitude, frequency, and time in the input fields and click the calculate button.

### What is a Simple Harmonic Motion?

Simple harmonic motion includes oscillating motion. A particle in this form of motion always takes the same path, accelerating towards a fixed location.

The simple pendulum is an excellent example of this. When a mass hanging on a string is moved away from its equilibrium position, it will bounce back and forth, accelerating towards the equilibrium point. If there is no energy loss, the pendulum will continue to swing indefinitely. The kinetic energy is at its highest at the equilibrium point.

### Simple Harmonic Motion Equations

It is possible to determine the particle's position, velocity, and acceleration at any moment in time if you know the period of oscillations. It's as simple as applying the following harmonic motion equations

y = A x sin(ωt)

v = A x ω x cos(ωt)

a = - A x ω² x sin(ωt)

- Where, A = amplitude of oscillations,
- y = displacement
- v = velocity
- a = acceleration
- ω = angular frequency of oscillations in rad/s. It can be calculated as ω = 2πf
- f = frequency
- t = time point when you measure the particle's displacement

### How to Find Out the Velocity and Acceleration of an Oscillating Particle?

The procedure for obtaining the oscillating particle's velocity, acceleration, and displacement is described below.

- Step 1: Examine an oscillating particle's amplitude, duration, frequency, and angular frequency.
- Step 2: Find the sine function of the angular frequency-time product.
- Step 3: To calculate the particle's displacement, multiply the result by amplitude.
- Step 4: Calculate the cos function of the angular frequency and time product.
- Step 5: To get the particle's velocity, multiply the result by the amplitude.
- Step 6: Multiply the angular frequency by the negative of the amplitude.
- Step 7: To get the acceleration, multiply the result by the value from step 2.

For more concepts check out physicscalculatorpro.comto get quick answers by using this free tool.

### Simple Harmonic Motion Examples

**Question 1:**The amplitude of a particle oscillating with a frequency of 1 Hz and a time of 1.8 seconds is 50 cm. How do you calculate the oscillating particle's angular frequency, displacement, acceleration, and velocity?

**Solution:**

Given: Amplitude A = 50 cm

Frequency f = 1 Hz

Time t = 1.8 sec

Angular Frequency ω = 2πf

= 2 x 3.14 x 1

= 6.28

y = A x sin(ωt)

= 50 x sin(6.28 x 1.8)

= 50 x sin(11.304)

= 50 x 0.196

= 9.8

v = A x ω x cos(ωt)

v = 50 x cos(6.28 x 1.8)

= 50 x cos(11.304)

= 50 x 0.98

= 49.03

a = -A x ω² x sin(ωt)

a = -50 x 6.28² x sin(6.28 * 1.8)

= -50 x 39.43 x sin(11.304)

= - 386.44

Therefore, the acceleration of the oscillating particle is - 386.44 mm/s², velocity is 49.03 mm/s, displacement is 9.8 mm.

### FAQs on Simple Harmonic Motion

**1. What are the characteristics of simple harmonic motion?**

Simple harmonic motion has the following main characteristics: The acceleration of a particle in simple harmonic motion is directly proportional to its displacement and directed towards its mean location. The particle's total energy is preserved as it moves in a simple harmonic motion. SHM is a motion that occurs regularly.

**2. What are the features of simple harmonic motion?**

Simple harmonic motion has the following key features: The acceleration of a particle in simple harmonic motion is directly proportional to its displacement and directed towards its mean location. The particle's total energy is preserved as it moves in a simple harmonic motion. SHM is a motion that occurs regularly.

**3. What are the SHM applications?**

Simple pendulum clocks, park swings, bungee jumps, musical instruments, automotive shock absorbers, and other real-world uses of Simple Harmonic Motion can be found.

**4. Define simple harmonic, periodic, and oscillation motion?**

Periodic motion is defined as a motion that repeats after an equal time interval and does not have an equilibrium position or restoring force. The oscillatory motion is a to and fro motion about the mean position that has an equilibrium position and a restoring force. SHM is a type of oscillation in which a straight line is drawn between two extreme points and has a restoring force and a mean position.