Two springs of spring constants k1 and k2 have equal maximum velocities. When executing simple harmonic motion, the ratio of their amplitudes (masses are equal) will be

Question

Two springs of spring constants k1 and k2 have equal maximum velocities. When executing simple harmonic motion, the ratio of their amplitudes (masses are equal) will be (A)  ( (k2/k1) )1/2  (B)  ( (k1/k2) )1/2  (C)  (k2/k1)  (D)  k1k2

Tardigrade Admin · Accepted Answer

The angular frequency of spring is given by ω =(√k/m) propto √k (because m=m1=m2 ) For equal maximum velocities, we have a1ω 1=a2ω 2 (a1/a2)=(ω 2/ω 1)=(√k2/k1)=( (k2/k1) )(1/2)

Q. Two springs of spring constants $k_{1}$ and $k_{2}$ have equal maximum velocities. When executing simple harmonic motion, the ratio of their amplitudes (masses are equal) will be

$(\frac{k _{2}}{k _{1}})^{1 / 2}$

$(\frac{k _{1}}{k _{2}})^{1 / 2}$

$\frac{k _{2}}{k _{1}}$

$k_{1} k_{2}$

The angular frequency of spring is given by $ω = \frac{k}{m} \propto k$ (because $m = m_{1} = m_{2}$ ) For equal maximum velocities, we have $a_{1} ω_{1} = a_{2} ω_{2}$ $\frac{a _{1}}{a _{2}} = \frac{ω _{2}}{ω _{1}} = \frac{k _{2}}{k _{1}} = (\frac{k _{2}}{k _{1}})^{\frac{1}{2}}$

Q. Two springs of spring constants k1​ and k2​ have equal maximum velocities. When executing simple harmonic motion, the ratio of their amplitudes (masses are equal) will be

(k1​k2​​)1/2

(k2​k1​​)1/2

k1​k2​​

k1​k2​