Answer to Question #99994 in Physics for Swapnil manoharrao Kamble

Question

Show that simple harmonic motion is isochronous

Answer 1

For simple harmonic motion

$$\frac{d^2x}{dt^2}+\omega^2x=0$$

$$x=A\cos{(\omega t+\phi)}$$

We can see that

$$\omega=const$$

Thus, simple harmonic motion is isochronous.