# Energy in SHM Calculator

The Energy in SHM Calculator will calculate:

1. Mechanical energy in a spring performing SHM
2. Kinetic and potential energy of an oscillating spring in a given instant when performing SHM
 🖹 Normal View🗖 Full Page View Calculator Precision (Decimal Places)0123456789101112131415 Amplitude of oscillation (A) m Period of oscillation (T) s Archimedes' constant (π) Time (t) s Mass of the oscillating object (m) kg Spring constant (k) N/m
Energy in SHM Calculator Results (detailed calculations and formula below)
The mechanical energy of an oscillating spring is J
The kinetic energy of the object attached to the spring is J
The potential energy of the object attached to the spring is J
Mechanical energy of an oscillating spring calculation
ME = k × A2/2
ME = × 2/2
ME = × /2
ME = /2
ME =
Kinetic and potential energy of an oscillating spring in a given instant when performing SHM calculation

### Kinetic energy of the object attached to the spring

KE = m × /T × A × (sin⁡/T × t)2/2
KE = × / × × (sin / × )2/2
KE = × × × (sin × )2/2
KE = × × × ( × )2/2
KE = × × × ()2/2
KE = × × × /2
KE = /2
KE =

### Potential energy of the object attached to the spring

PE = k × A × (cos /T × t)2/2
PE = × × (cos/ × )2/2
PE = × × (cos × )2/2
PE = × × ( × )2/2
PE = × × ()2/2
PE = × × /2
PE = /2
PE =
Input Values
Amplitude of oscillation (A) m
Period of oscillation (T) s
Archimedes' constant (π)
Time (t) s
Mass of the oscillating object (m) kg
Spring constant (k) N/m

Please note that the formula for each calculation along with detailed calculations are available below. As you enter the specific factors of each energy in SHM calculation, the Energy in SHM Calculator will automatically calculate the results and update the Physics formula elements with each element of the energy in SHM calculation. You can then email or print this energy in SHM calculation as required for later use.

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Section 6: Centre of Mass and Linear Momentum

Section 7: Rotation

## Using the Energy in SHM Calculator

The following restrictions and limatations apply when using the Energy in SHM Calculator.

1. Air resistance is not considered
2. Oscillations are taken as standing (sustainable)
4. The spring is taken as perfectly elastic

ME = k × A2/2

## Kinetic and potential energy of an oscillating spring in a given instant when performing SHM Formula and Calculation

### Kinetic energy of the object attached to the spring

KE = m × /T × A × (sin/T × t)2/2

### Potential energy of the object attached to the spring

PE = k × A × (cos /T × t)2/2

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