Question

A 2.25 kg mass on a string has a displacement as a function of time given by the equation: x (t) = 5.50 cm Cos(3.25 t). A) What is the force constant of the spring in N/m? B) What is the time for one complete vibration? C) Find the maximum speed of the object in m/s? D) What is the maximum force on the mass?

Answer 1

solution

comparing the standard equation

x (t) = x₀ cm Cos($\omega$t)

A)so force conatant

k=$m\omega^2=2.25\times(3.25)^2=23.75 N/m$

B)time

$t=\frac{2\pi}{\omega}=\frac{2\times3.14}{3.25}=1.93sec$

C)velocity is given

$v=\frac{dx}{dt}=-5.50\times3.25\sin(3.25t)$

here maximum velocity is v=0.1787 cm/sec

D)force is given

$F=m\frac{d^2x}{dt^2}=-2.25\times5.50\times3.25\times 3.25\cos(3.25t)$

so maximum force

$F=2.25\times5.50\times3.25\times 3.25=130.71N$