Question
Physics Question on simple harmonic motion
Two simple harmonic motions are represented by y1=5[sin2πt+3cos2πt]andy2=5sin(2πt+4π). The ratio of their amplitudes is
A
1:1
B
2:1
C
1:3
D
3:1
Answer
2:1
Explanation
Solution
Here, y1=5[sin2πt+3cos2πt] =10[21sin2πt+23cos2πt] =10[cos3πsin2πt+sin3πcos2πt] =10[sin(2πt+3π)] ∴A1=10 and y2=5sin(2πt+4π) ∴A2=5 Hence A2A1=510=12