Answer to Question #164640 in Mechanics | Relativity for Lucy green

Question

A mass is attached to a spring with a force constant of 40.0 N/m. The spring and mass are set to simple harmonic motion with a period of 0.50 s on a frictionless, horizontal surface.

a) What is the mass of the object?

b) What is the frequency of the oscillations?

c) At which point will the object be at maximum speed? Minimum speed?

d) At which point will the object be at max acceleration? Minimum acceleration?

Answer 1

(a) The mass of the object can be found from the formula:

$$T=2\pi\sqrt{\dfrac{m}{k}},$$ $$m=\dfrac{T^2k}{4\pi^2}=\dfrac{(0.5\ s)^2\cdot40\ \dfrac{N}{m}}{4\pi^2}=0.25\ kg.$$

(b) Let's find the frequency of the oscillations:

$$f=\dfrac{1}{T}=\dfrac{1}{0.5\ s}=2\ Hz.$$

(c) The object has maximum velocity at the equilibrium position (when $x=0$) and the minimum velocity at the extreme points (when $x=\pm A$).

(d) The object has maximum acceleration at the extreme points (when $x=\pm A$) and the minimum acceleration at the equilibrium position (when $x=0$).