A linear harmonic oscillator of force constant $2 \times 10^6\,Nm^{-1}$ and amplitude $0.01\, m$ has a total mechanical energy of $160\, J.$ Its
Diffcult
Download our app for free and get started
$A=0.01 m$
$k=2 \times 10^{6} N / m$
$E_{T}=160 J$
The total mechanical energy,
$E_{T}=(K . E)_{\max }+(P . E)_{\min }=160 J \ldots \ldots(1)$
we know that, maximum kinetic energy,
$(K . E)_{\max }=\frac{1}{2} k A^{2} \frac{1}{2} \times 2 \times 10^{6} \times 10^{-6}$
$(K . E)_{\max }=100 J$
from equation $(1),$
$(P . E)_{\min }=160-100=60 J$
The minimum kinetic energy is zero so, the maximum potential energy is $160 \mathrm{J}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A particle executing $SHM$ of amplitude $4\,cm$ and $T = 4s.$ The time taken by it to move from $+2\,cm$ to $+2\sqrt 3\,cm$ isView Solution
- 2A block of mass m, attached to a spring of spring constant $k$, oscillates on a smooth horizontal table. The other end of the spring is fixed to a wall. The block has a speed $v$ when the spring is at its natural length. Before coming to an instantaneous rest, if the block moves a distance $x$ from the mean position, thenView Solution
- 3A particle is doing simple harmonic motion of amplitude $0.06 \mathrm{~m}$ and time period $3.14 \mathrm{~s}$. The maximum velocity of the particle is. . . . .. . $\mathrm{cm} / \mathrm{s}$.View Solution
- 4A light pointer fixed to one prong of a tuning fork touches a vertical plate. The fork is set vibrating and the plate is allowed to fall freely. If eight oscillations are counted when the plate falls through $10 cm$, the frequency of the tuning fork is .... $Hz$View Solution
- 5Four massless springs whose force constants are $2k, 2k, k$ and $2k$ respectively are attached to a mass $M$ kept on a frictionless plane (as shown in figure). If the mass $M$ is displaced in the horizontal direction, then the frequency of oscillation of the system isView Solution
- 6A mass $m$ attached to free end of a spring executes SHM with a period of $1\; s$. If the mass is increased by $3\; kg$ the period of oscillation increases by one second, the value of mass $m$ is $..............kg$.View Solution
- 7A particle executes $S.H.M$ between $x =\, -A$ to $x =\, +A$ . The time taken for it in going from $0$ to $A/2$ is $T_1$ and from $A/2$ to $A$ is $T_2$. ThenView Solution
- 8View SolutionWhat will be the force constant of the spring system shown in the figure
- 9Values of the acceleration $A$ of a particle moving in simple harmonic motion as a function of its displacement $x$ are given in the table below. The period of the motion isView Solution
$A (mm \,\,s^{-2}$) $16$
$8$
$0$
$- 8$
$- 16$
$x\;(mm)$
$- 4$
$- 2$
$0$
$2$
$4$
- 10A body is performing simple harmonic with an amplitude of $10 \,cm$. The velocity of the body was tripled by air Jet when it is at $5 \,cm$ from its mean position. The new amplitude of vibration is $\sqrt{ x } \,cm$. The value of $x$ is________View Solution