Question:
Two simple harmonic motion, are represented by the equations $\mathrm{y}_{1}=10 \sin \left(3 \pi t+\frac{\pi}{3}\right)$
$\mathrm{y}_{2}=5(\sin 3 \pi \mathrm{t}+\sqrt{3} \cos 3 \pi \mathrm{t})$
Ratio of amplitude of $y_{1}$ to $y_{2}=x: 1$. The value of $x$ is
Solution:
$y_{1}=10 \sin \left(3 \pi t+\frac{\pi}{3}\right) \Rightarrow$ Amplitude $=10$
$y_{2}=5(\sin 3 \pi t+\sqrt{3} \cos 3 \pi t)$
$y_{2}=10\left(\frac{1}{2} \sin 3 \pi t+\frac{\sqrt{3}}{2} \cos 3 \pi t\right)$
$y_{2}=10\left(\cos \frac{\pi}{3} \sin 3 \pi t+\sin \frac{\pi}{3} \cos 3 \pi t\right)$
$\mathrm{y}_{2}=10 \sin \left(3 \pi \mathrm{t}+\frac{\pi}{3}\right) \Rightarrow$ Amplitude $=10$
So ratio of amplitudes $=\frac{10}{10}=1$
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
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- Atoms
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