Two SHMs are represented by the equations Y1=10 sin(3 πt+(π)/(4)) and Y2=5(sin3 πt+√(3) cos3 πt)

step 1 In this question we have given two simple harmonic motions and we have to find the amplitude rat

Two SHMs are represented by the equations Y1=10 sin(3...

Two SHMs are represented by the equations $Y_{1}=10$ $\sin \left(3 \pi t+\frac{\pi}{4}\right)$ and $Y_{2}=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t)$
Their amplitudes are in the ratio of
(A) $2: 1$
(B) $3: 1$
(C) $1: 3$
(D) $1: 4$

Key Concepts

Phase Shift

Phase shift in a sinusoidal function refers to the horizontal displacement of the wave from its standard position. It indicates the starting point of the oscillation relative to a reference and affects the timing of the cycle without altering the amplitude of the motion.

Sinusoidal Combination

Sinusoidal combination involves expressing a sum of sine and cosine functions, especially those with the same frequency, as a single sinusoid with a new amplitude and phase shift. This technique simplifies the analysis of oscillatory systems by consolidating multiple terms into one sinusoidal expression, making it easier to compare amplitudes and other characteristics.

Simple Harmonic Motion

Simple Harmonic Motion (SHM) is a type of periodic oscillatory motion where the restoring force acting on an object is directly proportional to its displacement from the equilibrium position. This motion is characterized by sinusoidal functions that describe the behavior of displacement, velocity, and acceleration over time.

Amplitude

Amplitude is the maximum displacement of an oscillating system from its equilibrium position. It quantifies the extent of the oscillation and is directly related to the energy contained in the motion. Even when the function includes phase shifts or is expressed as a combination of trigonometric functions, the amplitude represents the peak value of the oscillation.

Please give Ace some feedback