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 period of a mass $m$ attached to a spring of constant $k$ is given by $t = 2\pi \sqrt{\frac{m}{k}}$.Thus,$t_1 = 2\pi \sqrt{\frac{m}{k_1}}$ and

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) The period of a mass $m$ attached to a spring of constant $k$ is given by $t = 2\pi \sqrt{\frac{m}{k}}$.Thus,$t_1 = 2\pi \sqrt{\frac{m}{k_1}}$ 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 equivalent spring constant $k_{eq}$ is given by $\frac{1}{k_{eq}} = \frac{1}{k_1} + \frac{1}{k_2}$.The period of oscillation for the series combination is $T = 2\pi \sqrt{\frac{m}{k_{eq}}}$.Squaring this,$T^2 = 4\pi^2 \frac{m}{k_{eq}} = 4\pi^2 m \left( \frac{1}{k_1} + \frac{1}{k_2} \right)$.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

$A$ Wheatstone bridge is balanced. Find the ratio of electric power dissipated in $(P + Q)$ to $(R + S)$.

Four positive point charges $+q$ are kept at the four corners of a square of side $l$. The net electric field at the mid-point of any one side of the square is (Take,$\frac{1}{4 \pi \varepsilon_0}=k$)

Crossing over occurs between which of the following?

$A$ proton, a deuteron (nucleus of ${ }_1 H^2$) and an $\alpha$-particle with the same kinetic energy enter a region of uniform magnetic field moving at right angles to the field. The ratio of the radii of their circular paths is:

An insulated container contains $4 \, moles$ of an ideal diatomic gas at temperature $T$. Heat $Q$ is supplied to this gas,due to which $2 \, moles$ of the gas are dissociated into atoms,but the temperature of the gas remains constant. Then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module