Simple Harmonic Motion (SHM) Calculators
Understand oscillations with pendulums, springs, and SHM formulas.
Simple Pendulum Period Calculator
A simple pendulum consists of a mass attached to a string that swings back and forth.
m
m/s²
Time Period (T):
2.00 seconds
T = 2π × √(L / g) = 2 × 3.14159 × √(1 / 9.81) = 2.00 s
Spring-Mass System Calculator
A spring-mass system oscillates when displaced from equilibrium.
kg
N/m
Time Period (T):
0.99 seconds
T = 2π × √(m / k) = 2 × 3.14159 × √(0.5 / 20) = 0.99 s
Spring Constant Calculator
Calculate the spring constant using Hooke’s Law (F = kx).
N
m
Spring Constant (k):
40.00 N/m
k = F / x = 10 / 0.25 = 40.00 N/m
Displacement, Velocity & Acceleration Calculator
Calculate position, velocity, and acceleration for simple harmonic motion.
m
rad/s
s
Displacement x(t):
1.00 m
Velocity v(t):
0.00 m/s
Acceleration a(t):
-4.00 m/s²
x(t) = A × cos(ωt) = 1 × cos(2 × 0) = 1.00 m
v(t) = -Aω × sin(ωt) = -1 × 2 × sin(2 × 0) = 0.00 m/s
a(t) = -Aω² × cos(ωt) = -1 × 2² × cos(2 × 0) = -4.00 m/s²
v(t) = -Aω × sin(ωt) = -1 × 2 × sin(2 × 0) = 0.00 m/s
a(t) = -Aω² × cos(ωt) = -1 × 2² × cos(2 × 0) = -4.00 m/s²
Angular SHM Calculator
Calculate time period for torsional pendulum and other angular oscillators.
kg·m²
N·m/rad
Time Period (T):
3.14 seconds
T = 2π × √(I / κ) = 2 × 3.14159 × √(0.5 / 2) = 3.14 s