1. A 5.0-g mass is sandwiched between two springs with spring constants K1 and K
ID: 1365549 • Letter: 1
Question
1. A 5.0-g mass is sandwiched between two springs with spring constants K1 and K2. The mass is displaced 10 cm from its quilibrium postion and makes sixteen complete oscillations in 1s with no loss of mechanical energy. Calculate the period of the motion T, the angular frequency w, the sum of the spring constants k1+k2, and the mechanical energy E of the oscillator.
2. The experiement is repeated, this time displacing the mass only one centimeter from the equilibrium postition. Calculate the angular frequency w of the motion and the mechanical energy E of the oscillator.
Explanation / Answer
Q1. 16 complete oscillations in 1 second.
==>time period for one oscillation=1/16 second
==>frequency=1/time period=1/(1/16)=16 Hz
angular frequency=2*pi*frequency=100.531 rad/sec
as angular frequency=sqrt((k1+k2)/mass)
==>sqrt((k1+k2)/0.005)=100.531
==>(k1+k2)/0.005=100.531^2
==>k1+k2=50.532 N/m
mechanical energy=0.5*(k1+k2)*amplitude^2
=0.5*50.532*0.1^2
=0.25266 J
Q2.
as angular frequency does not depend upon the amplitude, it will remain same as 100.531 rad/sec
mechanical energy=0.5*(k1+k2)*0.01^2=0.5*50.532*0.01^2=2.5266*10^(-3) J
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