A particle at the end of a spring executes si | vedclass

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

Question

(B) The time period of a spring-mass system is given by $t = 2\pi \sqrt{\frac{m}{k}}$.For the two springs,we have $t_1 = 2\pi \sqrt{\frac{m}{k_1}}$ an

Vedclass · Accepted Answer

$T^2 = t_1^2 + t_2^2$

Vedclass · Answer

(B) The time period of a spring-mass system is given by $t = 2\pi \sqrt{\frac{m}{k}}$.For the two springs,we have $t_1 = 2\pi \sqrt{\frac{m}{k_1}}$ and $t_2 = 2\pi \sqrt{\frac{m}{k_2}}$.Squaring these,we get $t_1^2 = 4\pi^2 \frac{m}{k_1}$ and $t_2^2 = 4\pi^2 \frac{m}{k_2}$.When two springs are connected in series,the effective spring constant $k$ is given by $\frac{1}{k} = \frac{1}{k_1} + \frac{1}{k_2}$,which implies $k = \frac{k_1 k_2}{k_1 + k_2}$.The time period $T$ for the series combination is $T = 2\pi \sqrt{\frac{m}{k}}$.Squaring this,$T^2 = 4\pi^2 \frac{m}{k} = 4\pi^2 m \left( \frac{1}{k} \right) = 4\pi^2 m \left( \frac{1}{k_1} + \frac{1}{k_2} \right)$.Substituting the expressions for $t_1^2$ and $t_2^2$,we get $T^2 = 4\pi^2 \frac{m}{k_1} + 4\pi^2 \frac{m}{k_2} = t_1^2 + t_2^2$.

$A$ particle at the end of a spring executes simple harmonic motion with a period $t_1$,while the corresponding period for another spring is $t_2$. If the period of oscillation with the two springs in series is $T$,then

Similar Questions

The force-deformation equation for a nonlinear spring fixed at one end is $F = 4x^{1/2}$,where $F$ is the force (expressed in newtons) applied at the other end and $x$ is the deformation expressed in meters.

The time period of simple harmonic motion of mass $M$ in the given figure is $\pi \sqrt{\frac{\alpha M}{5 K}}$,where the value of $\alpha$ is . . . . . . .

$A$ mass $M$ is suspended from a light spring. An additional mass $M_1$ added extends the spring further by a distance $x$. Now the combined mass will oscillate on the spring with period $T=$

Two identical springs of constant $K$ are connected in series and parallel as shown in the figure. $A$ mass $M$ is suspended from them. The ratio of their frequencies in series to parallel combination will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module