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A particle moves along the X-axis according to the equation x = 10 sin^3 (πt). The amplitudes and frequencies of components SHMs are (A) amplitude 30/4, 10/4 ; frequencies 3/2, 1/2(B) amplitude 30/4. 10/4 ; frequencies 1/2, 312 C) amplitude 10, 1O ; frequencies 1/2, 1/2(D) amplitude 30/4. 10 ; frequencies 3/2, 2

A particle moves along the X-axis according to the equation x = 10 sin^3 (πt). The amplitudes and frequencies of components SHMs are (A) amplitude 30/4, 10/4 ; frequencies 3/2, 1/2(B) amplitude 30/4. 10/4 ; frequencies 1/2, 312 C) amplitude 10, 1O ; frequencies 1/2, 1/2(D) amplitude 30/4. 10 ; frequencies 3/2, 2

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Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
Write,  x = sin^3 (πt) in simple trignometric form:
x = (3/4)sin(pi*t) – (sin(3*pi*t))/4
Hence it is the superimpostion of two SHM waves.
Amplitude net = > A1 + A2 = > ¾ + (-1/4) = > ½
             and    => A 1- A2 => ¾ + ¼ = 1
and Frequecnies = > ½ + 3/2 = > 2 and 1
 

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