The variation of potential energy U of a harm | vedclass

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

Question

(B) From the given figure,the potential energy $U$ is given by $U = U_0 + \frac{1}{2}Ky^2$,where $U_0$ is the minimum potential energy at $y = 0$.At $

Vedclass · Accepted Answer

$150 	ext{ Nm}^{-1}$

Vedclass · Answer

(B) From the given figure,the potential energy $U$ is given by $U = U_0 + \frac{1}{2}Ky^2$,where $U_0$ is the minimum potential energy at $y = 0$.At $y = 0$,$U_{\min} = 0.01 	ext{ J}$.At $y = 20 	ext{ mm} = 20 	imes 10^{-3} 	ext{ m} = 2 	imes 10^{-2} 	ext{ m}$,$U_{\max} = 0.04 	ext{ J}$.The change in potential energy is $\Delta U = U_{\max} - U_{\min} = \frac{1}{2}Ky^2$.Substituting the values:$0.04 	ext{ J} - 0.01 	ext{ J} = \frac{1}{2} 	imes K 	imes (2 	imes 10^{-2} 	ext{ m})^2$$0.03 	ext{ J} = \frac{1}{2} 	imes K 	imes 4 	imes 10^{-4} 	ext{ m}^2$$0.03 = K 	imes 2 	imes 10^{-4}$$K = \frac{0.03}{2 	imes 10^{-4}} = \frac{3 	imes 10^{-2}}{2 	imes 10^{-4}} = 1.5 	imes 10^2 	ext{ Nm}^{-1} = 150 	ext{ Nm}^{-1}$.

The variation of potential energy $U$ of a harmonic oscillator with respect to displacement $y$ is as shown in the figure. Find the spring constant $K$.

Similar Questions

$A$ mass suspended from a vertical spring performs $S.H.M.$ with a period of $T = 0.1 \ s$. The spring is unstretched at the highest point of its motion. What is the maximum speed of the mass? (Take gravitational acceleration $g = 10 \ m/s^2$)

Initially,the system is in equilibrium. The time period of $SHM$ of the block in the vertical direction is

$A$ mass $M$ is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes $S.H.M.$ of period $T$. If the mass is increased by $m$,the time period becomes $\frac{5T}{3}$. What is the ratio $\left(\frac{M}{m}\right)$?

The frequency of oscillations of a mass $m$ connected horizontally by a spring of spring constant $k$ is $4 \ Hz$. When the spring is replaced by two identical springs connected in series as shown in the figure,the effective frequency is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module