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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
Energy in SHM Calculator
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 × 2π/T × A × (sin⁡2π/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 2π/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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Discover Physics with free Physics Revision Notes and Physics Calculator: Energy in SHM. This image shows the properties and energy in SHM formula for the Energy in SHM. This calculator will calculate mechanical energy in a spring performing SHM and kinetic and potential energy of an oscillating spring in a given instant when performing SHM

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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)
  3. The thread is non-stretchable
  4. The spring is taken as perfectly elastic

Mechanical energy of an oscillating spring Formula and Calculation

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 × 2π/T × A × (sin2π/T × t)2/2

Potential energy of the object attached to the spring

PE = k × A × (cos 2π/T × t)2/2

Oscilations Physics Tutorials associated with the Uniform Motion Calculator

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