A force of $6.4\, N$ stretches a vertical spring by $0.1 \,m$. The mass that must be suspended from the spring so that it oscillates with a period of $\left( {\frac{\pi }{4}} \right)sec$. is ... $kg$
Medium
Download our app for free and get started
(b) Force constant of a spring is given by $F = kx$
$6.4 = k(0.1)$ or $k = 64N/m$
$T = 2\pi \sqrt {\frac{m}{k}} $ ==> $\frac{\pi }{4} = 2\pi \sqrt {\frac{m}{{64}}} $; $\frac{m}{{64}} = {\left( {\frac{1}{8}} \right)^2}$; $m = 1kg$
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
- 1The length of the second pendulum on the surface of earth is $1\, m$. The length of seconds pendulum on the surface of moon, where g is 1/6th value of $g$ on the surface of earth, isView Solution
- 2The variation of the acceleration $a$ of the particle executing $S.H.M.$ with displacement $x$ is as shown in the figureView Solution
- 3The equation of motion of a particle of mass $1\,g$ is $\frac{{{d^2}x}}{{d{t^2}}} + {\pi ^2}x = 0$ where $x$ is displacement (in $m$ ) from mean position. The frequency of oscillation is .... $s$ (in $Hz$ )View Solution
- 4$Assertion :$ In simple harmonic motion, the velocity is maximum when the acceleration is minimum.View Solution
$Reason :$ Displacement and velocity of $S.H.M.$ differ in phase by $\frac{\pi }{2}$ - 5An object of mass $0.2\, kg$ executes simple harmonic along $X-$ axis with frequency of $\frac{{25}}{\pi }Hz$. At the position $x = 0.04m$, the object has kinetic energy of $0.5 \,J$ and potential energy of $0.4\, J$ amplitude of oscillation in meter is equal toView Solution
- 6A block of mass $m$ is having two similar rubber ribbons attached to it as shown in the figure. The force constant of each rubber ribbon is $K$ and surface is frictionless. The block is displaced from mean position by $x\,cm$ and released. At the mean position the ribbons are underformed. Vibration period isView Solution
- 7A particle is executing Simple Harmonic Motion $(SHM)$. The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will beView Solution
- 8A simple pendulum, suspended from the ceiling of a stationary van, has time period $T$. If the van starts moving with a uniform velocity the period of the pendulum will beView Solution
- 9If the time period of a two meter long simple pendulum is $2\, s$, the acceleration due to gravity at the place where pendulum is executing $S.H.M.$ isView Solution
- 10A simple pendulum is suspended in a car. The car starts moving on a horizontal road according to equation $x\, = \,\frac{g}{2}\,\sqrt 3 {t^2}$. Find the time period of oscillation of the pendulum.View Solution