Problem — Maximum velocity and acceleration

Problem

A harmonic oscillator has mass $m = 0{,}50\;\text{kg}$, elastic constant $K = 18\;\text{N/m}$ and amplitude $A = 0{,}050\;\text{m}$. Determine the maximum velocity and maximum acceleration of the motion.

Solution

The angular frequency of the system is:

$\omega = \sqrt{\frac{K}{m}} = \sqrt{\frac{18}{0{,}50}} = \sqrt{36} = 6\;\text{rad/s}$

The maximum velocity occurs at the passage through equilibrium and equals $v_{\max} = A\omega$:

$v_{\max} = 0{,}050 \cdot 6\;\text{m/s} = 0{,}30\;\text{m/s}$

$\ev{v_{\max} = 0{,}30\;\text{m/s}}$

The maximum acceleration occurs at the endpoints of the motion and equals $a_{\max} = A\omega^2$:

$a_{\max} = 0{,}050 \cdot 36\;\text{m/s}^2 = 1{,}8\;\text{m/s}^2$

$\ev{a_{\max} = 1{,}8\;\text{m/s}^2}$

Links

Topics: Oscillations and harmonic motion Concepts: Simple harmonic motion Objects: Spring