Question

10. A 1.5 kg mass is attached to the end set into simple harmonic motion wit ned to the end of a horizontal spring of spring constant 60 N/m and a. What is the maximum potential energy of the system? b. What is the frequency of vibration? c. What is the period of vibration?

Answer 1

10. Let us considere a mass m attached to the end of a hore zonal spring of spring constant k K m from Hook's Raw the force acting on the mass mis = – KQ Equation of motion of the system is mda dti --ki

dtr twtx=0 Where was a This is the equation of simple harmonic oscillaton. solution of this equation is x= Asimwt i. The motion of the mass m is simple. harmonic motion with amplitude A. worek done da is to create a small displacement dw =-F da =tunda F=- KR displacement from o to xis Worch done fore the w = tfunda 2 - 2xx This work done, is stored in the form of potential energy in the system = 8k x²

u=&K A sinkut The potential energy is maximum when sin wt = 1 . Umax 4gh

= 2 x (60) * (0.7532 K=60N/m A=0.75 m = 16.875J i Maximum potential energy of the system 16.875J from w is the angulare 21 f = hh freeque ney I m = 1.5kg a Gora f = 1.006 Hz in the freequency of vibration is 10000 Hz w= dk is the Again, if T w period of vibreation then T= 21 m = + = 100E = 0.9945 n. The period of vibration is 0.9948