A 5.0-g mass if sandwiched between two springs with spring constant k1 aand k2.

Question

A 5.0-g mass if sandwiched between two springs with spring constant k1 aand k2. The mass is didplaced 10 cm from its equilibrium position and makes sixteen complete oscillations in 1 s with no loss of mechanical energy. Calculate the period of the motion T, the angular frequency ?, the sum of the spring constants k1+k2 , and the mechanical energy E of the oscillator.

(2) The experiment is repeated, this time displacing the mass only one centimeter from the equilibrium position. Calculate the angular frequency ? of the motion and the mechanical energy E of the oscillator.

Explanation / Answer

frequency =16Hz

time period = 1/16=0.0625s

angular frequency =2*pi*f = 2*3.14*16=100.53

since the spring are in parallel their equivalent K =k1+k2

T=2pi*sqrt(m/k1+k2)

0.0625= 2*3.14 *sqrt(0.005/k1+k2)

k1+k2=50.53N/m

ME=1/2kx^2=1/2*50.53*0.1^2=0.2526J

2)for 1cm displaceemnt

w will remain same

ME=1/2kx^2=1/2*50.53*0.01^2=2.5265*10^-3J

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