Question

a 1.25kg mass on a pring vibrates as simple harmonic oscillator with time dependant position y, y(t)=(0.250m)vos(12.1t)
find:
a. amplitude im meter
b.frequency of oscillation in hertz
c.period of osillation in s
d.position at t=1.4s
e.velocity at t=1.4s
f.spring constant k

Answer 1

Given, the equation of motion of mass is

                                  

The general equation of wave traveling in positive x-direction is

                                  

Where A is amplitude, is angular frequency of the wave, k is wave number.

So, for the given mass sprng system,

a. Amplitude of the mass is 0.250 m.

b. Angular frequency is

                                

                      or,                 (since )

                      or,     

Hence, the frequency of oscillation of the mass is 1.93 Hz.

c. Period of oscillation is

                            

d. Position at 1.4 second is

                             

e. The velocity of the mass is

                                 

So, velocity of particle at 1.4 second is

                                

f. The angular frequency in spring mass system is given by

                               

Where K is spring constant, and m is mass.

Putting all the values, we can write