a particle is executing shm with total mechanical energy 90 J and amplitude 6cm. if its energy is somehow decreased to 40J then its amplitude will become ?

Question

apoorvk · Answer

Which form of mechanical energy is usually expressed in terms of the amplitude - check that out. Now use simple unitary method, and find out the new amplitude!

Let me know if you need me to clearer. Season's Greetings! :]

anonymous · Answer

Is the particle on a spring or a pendulum? Total mechanical energy is given by 1/2kA^2 where K is the constant of the system and A is the amplitude.

fifciol · Answer

Total mechanical energy is given by the equation:
$$E_1=\frac{ kA_1^2 }{ 2 }$$where E1=90J and A1=6cm
So you are able to determine constant k:
$$k=\frac{ 2E_1 }{ A_1^2 }$$
You know that 
$$E_2=\frac{ kA_2^2 }{ 2 }$$ where E2=40J and A2 is your unknown, so
$$A_2^2=\frac{ 2E_2 }{ k }=2E_2\frac{ A_1^2 }{ 2E_1}=A_1^2\frac{ E_2 }{ E_1 }$$ so $$A_2=A_1\sqrt{\frac{ E_2 }{ E_1 }}$$

anonymous · Answer

agree with Fifciol