A mass m is suspended separately by two sprin | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For a spring-mass system,the time period is given by $T = 2\pi \sqrt{\frac{m}{k}}$.In the first case,for spring $k_1$,the time period is $T_1 = 2\

Vedclass · Accepted Answer

$T^{-2} = T_1^{-2} + T_2^{-2}$

Vedclass · Answer

(B) For a spring-mass system,the time period is given by $T = 2\pi \sqrt{\frac{m}{k}}$.In the first case,for spring $k_1$,the time period is $T_1 = 2\pi \sqrt{\frac{m}{k_1}}$. Squaring both sides,we get $T_1^2 = 4\pi^2 \frac{m}{k_1}$,which implies $\frac{1}{T_1^2} = \frac{k_1}{4\pi^2 m}$.In the second case,for spring $k_2$,the time period is $T_2 = 2\pi \sqrt{\frac{m}{k_2}}$. Squaring both sides,we get $T_2^2 = 4\pi^2 \frac{m}{k_2}$,which implies $\frac{1}{T_2^2} = \frac{k_2}{4\pi^2 m}$.When the two springs are connected in parallel,the effective spring constant is $k_{eff} = k_1 + k_2$. The time period $T$ is given by $T = 2\pi \sqrt{\frac{m}{k_1 + k_2}}$.Squaring both sides,we get $T^2 = 4\pi^2 \frac{m}{k_1 + k_2}$,which implies $\frac{1}{T^2} = \frac{k_1 + k_2}{4\pi^2 m}$.Substituting the expressions for $\frac{k_1}{4\pi^2 m}$ and $\frac{k_2}{4\pi^2 m}$,we get $\frac{1}{T^2} = \frac{1}{T_1^2} + \frac{1}{T_2^2}$.This can be written as $T^{-2} = T_1^{-2} + T_2^{-2}$.

Similar Questions

On a smooth inclined plane,a body of mass $M$ is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has a force constant $K$,the period of oscillation of the body (assuming the springs are massless) is

To make the frequency of an oscillator double,we have to

$A$ block of mass $m$ is suspended separately by two different springs having time periods $t_1$ and $t_2$. If the same mass is connected to a parallel combination of both springs,then its time period will be

$A$ system consisting of three masses attached to a spring is in equilibrium. When the $700\,g$ mass is removed,the system oscillates with a period of $3\,s$. When the $500\,g$ mass is also removed,what will be the new time period of the system? (in $\text{seconds}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module