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Simple Harmonic Oscillation

the amplitude...

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the amplitude of simple harmonic motion obtained by combining the motions x1=2sin wt x2= 4sin(wt+pi/6) x3=6sin(wt+pi/3)is

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Q. What will be the displacement equation of the simple harmonic motion obtained by combining the motions?

x_{1} = 2 sin ω t

x_{2} = 4 sin (ω t + \frac{π}{6})

x_{3} = 6 sin (ω t + \frac{π}{3})

Q. Two simple harmonic motions are given by

x_{1} = \frac{a}{2} sin ω t + \frac{\sqrt{3} a}{2} cos ω t

x_{2} = a sin ω t + a cos ω t

. What is the ratio of the amplitude of the first motion to that of the second ?

Q. Two simple harmonic motions are given by:

x_{1} = a sin ω t + a cos ω t

x_{2} = a sin ω t + \frac{a}{\sqrt{3}} cos ω t

The ratio of the amplitudes of first and second motion and the phase difference between them are respectively:

Q. The resultant amplitude due to superposition of three simple harmonic motions

x_{1} = 3 sin ω t

x_{2} = 5 sin (ω t + 37^{\circ})

x_{3} = - 15 cos ω t

Q. A simple harmonic motion is represented by

y = 5 (sin 3 π t + \sqrt{3} cos 3 π t) c m

The amplitude and time period of the motion are :

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