Oscillations
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Question : 10
Total: 25
In previous question let us take the position of mass when the spring is unstretched as x = 0, and the direction from left to right as the positive direction of x-axis. Give x as a function of time t for the oscillating mass if at the moment we start the stopwatch (t = 0), the mass is
(a) at the mean position,
(b) at the maximum stretched position, and
(c) at the maximum compressed position.
In what way do these functions for simple harmonic motion differ from each other, in frequency, in amplitude or the initial phase?
(a) at the mean position,
(b) at the maximum stretched position, and
(c) at the maximum compressed position.
In what way do these functions for simple harmonic motion differ from each other, in frequency, in amplitude or the initial phase?
Solution:
From previous solution,
A = 2.0 cm ; ω = √
= √
= 20 s − 1
(a) As time is noted from the mean position, hence using
x = A sin ω t x = 2 sin 20 t
(b) At maximum stretched position, the mass is at the extreme right position, with an initial phase of
x = A sin ( ω t +
) = A cos ω t = 2 cos 20 t
(c) At maximum compressed position, the mass is at the extreme left position, with an initial phase of
x = A sin ( ω t +
) = − A cos ω t = − 2 cos 20 t
These functions neither differ in amplitude nor in frequency. They differ in initial phase.
(a) As time is noted from the mean position, hence using
(b) At maximum stretched position, the mass is at the extreme right position, with an initial phase of
(c) At maximum compressed position, the mass is at the extreme left position, with an initial phase of
These functions neither differ in amplitude nor in frequency. They differ in initial phase.
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