modern physics 1. A mass moves along the x-axis under the influence of spring wh

Question

modern physics

1. A mass moves along the x-axis under the influence of spring whose equilibrium position is at the origin. The mass moves between limits of -10 cm and +10 cm, and the period of its motion is 3 s. (a) What is the period if the mass is doubled? (b) What is the period is the amplitude is halved to 5 cm? Show clearly how you get the answers. 2. A mass of 1.2 kg attached to a spring, is in simple harmonic motion along the x-axis, and its period is T= 2.5 s. If the total energy of the spring and mass system is 2.7 J, what is the amplitude of the oscillation?

Explanation / Answer

(A) For Spring mass system ,

Time period, T = 2 pi sqrt( m / k)

if m is doubled then

then T will become sqrt(2) times.

T' = sqrt(2) T = 1.414 x 3 = 4.24 sec .....Ans

(B) period of independentof apmlitude.

hence time period will remain same.

T = 3 sec

..............................................................

2. T = 2pi sqrt( m / k)

(2.5 / 2pi)^2 = 1.2 / k

k = 7.6 N/m

total energy = k A^2 / 2

2.7 = 7.6 A^2 / 2

A = 0.84 m ......Ans

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