How do you calculate the maximum speed in simple harmonic motion?

To calculate the maximum speed in simple harmonic motion, use the formula v_max = Aω.

In simple harmonic motion, an object oscillates back and forth around a central equilibrium point. The displacement of the object from this point can be described by the equation x = A sin(ωt), where A is the amplitude of the motion and ω is the angular frequency.

The velocity of the object can be found by taking the derivative of the displacement equation with respect to time: v = dx/dt = Aω cos(ωt). The maximum velocity occurs when cos(ωt) = 1, which happens when ωt = 0 or 2π. Therefore, the maximum velocity is v_max = Aω.

It's important to note that the maximum velocity occurs at the equilibrium point, where the displacement is zero. At this point, all of the potential energy of the system has been converted to kinetic energy, resulting in the maximum speed. As the object moves away from the equilibrium point, the speed decreases until it reaches zero at the maximum displacement.

In summary, the maximum speed in simple harmonic motion can be calculated using the formula v_max = Aω, where A is the amplitude of the motion and ω is the angular frequency. This maximum speed occurs at the equilibrium point, where all potential energy has been converted to kinetic energy.