Simple Harmonic Motion Calculator
Calculate position, velocity, acceleration, and energy for simple harmonic motion. Analyze oscillating systems.
System Parameters
0.5 m
0.01 m5 m
m
1 kg
0.1 kg100 kg
kg
100 N/m
1 N/m1,000 N/m
N/m
0 s
0 s10 s
s
0°
0°360°
°
Position at t = 0s
0.5000 m
vVelocity
0.0000 m/s
aAcceleration
-50.0000 m/s²
TPeriod
0.6283 s
fFrequency
1.5915 Hz
ωAngular Frequency
10.0000 rad/s
vMax Velocity
5.0000 m/s
Energy Distribution:
Kinetic
0.0000 J
Potential
12.5000 J
Total
12.5000 J
Key Equations:
x(t) = A cos(ωt + φ)
ω = √(k/m) = 10.0000 rad/s
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. Common examples include a mass on a spring, a simple pendulum (for small angles), and oscillating molecules. SHM is characterized by sinusoidal oscillation with constant amplitude and frequency in the absence of friction.
SHM Equations
Position
x(t) = A cos(ωt + φ)
Velocity
v(t) = -Aω sin(ωt + φ)
Acceleration
a(t) = -Aω² cos(ωt + φ)
Period
T = 2π√(m/k)