(A) Given: Mass $m = 1 \ kg$,spring constant $k = 100 \ N \ m^{-1}$,amplitude $A = 10 \ cm = 0.1 \ m$,displacement $x = 5 \ cm = 0.05 \ m$.Angular fre

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(A) Given: Mass $m = 1 \ kg$,spring constant $k = 100 \ N \ m^{-1}$,amplitude $A = 10 \ cm = 0.1 \ m$,displacement $x = 5 \ cm = 0.05 \ m$.Angular frequency $\omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{100}{1}} = 10 \ rad \ s^{-1}$.Velocity at displacement $x$ is given by $v = \omega \sqrt{A^2 - x^2} = 10 \sqrt{0.1^2 - 0.05^2} = 10 \sqrt{0.01 - 0.0025} = 10 \sqrt{0.0075} = 10 \times 0.0866 = 0.866 \ m \ s^{-1}$.Kinetic energy $K.E. = \frac{1}{2} m v^2 = \frac{1}{2} \times 1 \times (0.866)^2 = 0.5 \times 0.75 = 0.375 \ J$.Potential energy $P.E. = \frac{1}{2} k x^2 = \frac{1}{2} \times 100 \times (0.05)^2 = 50 \times 0.0025 = 0.125 \ J$.

Class 11 Physics Oscillations SHM of Spring Mass System

Medium

$A$ block of mass $1 \ kg$ is fastened to a spring of spring constant $100 \ N \ m^{-1}$. The block is pulled to a distance $x = 10 \ cm$ from its equilibrium position $(x = 0 \ cm)$ on a frictionless surface,from rest at $t = 0$. The kinetic energy and the potential energy of the block when it is $5 \ cm$ away from the mean position are:

AP EAMCET 2021 All AP EAMCET

A
$0.375 \ J, 0.125 \ J$
B
$0.125 \ J, 0.375 \ J$
C
$0.125 \ J, 0.125 \ J$
D
$0.375 \ J, 0.375 \ J$

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Three blocks of masses $700 \,g$,$500 \,g$,and $400 \,g$ are suspended at the end of a spring as shown in the figure and are in equilibrium. When the $700 \,g$ block is removed,the system has a period of oscillation of $3 \,s$. If both $700 \,g$ and $500 \,g$ blocks are removed,the period of oscillation becomes

DifficultAP EAMCET 2020

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Two bodies $M$ and $N$ of equal masses are suspended from two separate massless springs of force constants $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal,the ratio of the amplitude of $M$ to that of $N$ is

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