A block of mass m,attached to a spring of spr | vedclass

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

Question

(C) The block is in simple harmonic motion. When the spring is at its natural length,the block is at the mean position,and its kinetic energy is maxim

Vedclass · Accepted Answer

$x = v \sqrt{m/k}$

Vedclass · Answer

(C) The block is in simple harmonic motion. When the spring is at its natural length,the block is at the mean position,and its kinetic energy is maximum.At the mean position,the total energy is purely kinetic: $E = \frac{1}{2}mv^2$.At the extreme position,the block comes to an instantaneous rest,and the total energy is purely potential: $E = \frac{1}{2}kx^2$.By the law of conservation of mechanical energy,the total energy at the mean position equals the total energy at the extreme position:$\frac{1}{2}mv^2 = \frac{1}{2}kx^2$Solving for $x$:$x^2 = \frac{m}{k}v^2$$x = v\sqrt{\frac{m}{k}}$

Similar Questions

The scale of a spring balance which can measure from $0$ to $15 \ kg$ is $0.25 \ m$ long. If a body suspended from this balance oscillates with a time period $\frac{2 \pi}{5} \ s$,neglecting the mass of the spring,find the mass of the body suspended. (in $kg$)

$A$ mass $m$ is suspended separately by two different springs of spring constant $K_1$ and $K_2$ giving the time periods $t_1$ and $t_2$ respectively. If the same mass $m$ is connected by both springs as shown in the figure,then the time period $t$ is given by the relation:

$A$ $100 \,g$ mass stretches a particular spring by $9.8 \,cm$,when suspended vertically from it. How large a mass must be attached to the spring if the period of vibration is to be $6.28 \,s$?

$A$ particle of mass $m$ is attached to three identical springs $A, B$ and $C$ each of force constant $k$ as shown in the figure. If the particle of mass $m$ is pushed slightly against the spring $A$ and released,then the time period of oscillations is

$A$ mass $m$ attached to a spring oscillates every $2 \, s$. If the mass is increased by $2 \, kg$,then the time period increases by $1 \, s$. The initial mass is ..... $kg$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module