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the equation of SHM is given as X=3sin20πt+4cos20πtWhere X is in cm and t is in second.the amplitude is---Explain???

the equation of SHM is given as X=3sin20πt+4cos20πtWhere X is in cm and t is in second.the amplitude is---Explain???

Grade:11

1 Answers

Kshitij Sharma
33 Points
7 years ago
using  identity:   asiny+bcosy=\sqrt{a^{2}+b^{2}}sin(y+\alpha)                                                                                                                          where \tan\alpha=b/a
the equation of SHM reduces to  \sqrt{3^{2}+4^{2}}\sin(20\pi t+\alpha )​ = 5sin(20\pit+\alpha)
Hence, amplitude is 5 c.m. ​
 
 
 
 

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