Question

Q5. two springs of constants k1 and k2 have equal maximum velocities when
executing SHM. The ratio of their amplitudes will be (masses are equal)-​

Answer 1

Question :

Two springs of constants k1 and k2 have equal maximum velocities when executing SHM,the ratio of their amplitudes will be (masses are equal) :

Solution :

• The springs have equal maximum velocities and masses

• Their springs constants are $\sf K_1 \ \sf{and} \ K_2$

Maximum Velocity is given by :

$\sf \: \: v {}_{max} = A \omega$

Also,

$\sf \: \omega \: = \sqrt{ \dfrac{k}{m} }$

Thus,

$\sf \: v = {A}_{1} \times \sqrt{ \dfrac{ K_{1} }{M} } - - - - - - - (1)$

Also,

$\sf \: v = A_{2} \times \sqrt{ \dfrac{ K_{2} }{M} } - - - - - - -(2)$

Equating equations (1) and (2),as maximum velocities of the SHM are equal

$\longrightarrow \: \sf \: A_{1} \times \sqrt{ \dfrac{ K_{1} }{M} } = A_{2} \times \sqrt{ \dfrac{ {K}_{2} }{M} } \\ \\ \longrightarrow \: \sf{ \dfrac{ A_{1} }{ A_{2} } = \sqrt{ \dfrac{ K_{2} }{ K_{1} } } } \\ \\ \longrightarrow \: \boxed{ \boxed{\sf{ \dfrac{ A_{1} }{ A_{2} } = (\frac{ K_{1} }{ {K}_{2} } ) {}^{ \frac{1}{2} } }}}$