Mark the wrong statement.

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

Question

(B) For $S.H.M.$,the force on the particle is given by $F = -kx$.Since $F = ma$,we have $ma = -kx$,which implies $a = -(k/m)x$.Comparing this with the

Vedclass · Accepted Answer

All motions having the same time period are $S.H.M.$

Vedclass · Answer

(B) For $S.H.M.$,the force on the particle is given by $F = -kx$.Since $F = ma$,we have $ma = -kx$,which implies $a = -(k/m)x$.Comparing this with the standard $S.H.M.$ equation $a = -\omega^2 x$,we get $\omega^2 = k/m$,which is a constant.Since the angular frequency $\omega$ is constant,the time period $T = 2\pi/\omega$ is also constant. Thus,statement $A$ is correct.Not all periodic motions are $S.H.M.$ For example,uniform circular motion has a fixed time period but is not $S.H.M.$ because the force is not proportional to displacement. Thus,statement $B$ is incorrect.The total energy of $S.H.M.$ is given by $E = (1/2)kA^2$,which shows that energy is directly proportional to the square of the amplitude $(A^2)$. Thus,statement $C$ is correct.The displacement equation is $x = A \sin(\omega t + \phi)$,where $\phi$ is the phase constant. The value of $\phi$ is determined by the initial position and velocity of the particle at $t = 0$. Thus,statement $D$ is correct.Therefore,the wrong statement is $B$.

Similar Questions

What is the importance of periodic $\text{sine}$ and $\text{cosine}$ functions in physics?

$A$ point particle of mass $0.1\, kg$ is executing $S.H.M.$ with an amplitude of $0.1\, m$. When the particle passes through the mean position,its kinetic energy is $8 \times 10^{-3} \, J$. Obtain the equation of motion of this particle if the initial phase of oscillation is $45^o$.

Define simple harmonic motion and write its important characteristics.

$A$ $S.H.M.$ is represented by $x = 5\sqrt{2} (\sin 2\pi t + \cos 2\pi t).$ The amplitude of the $S.H.M.$ is .... $cm$.

Write the force law for $SHM$ and obtain the formula for the period of an $SHM$ particle.

Vedclass Test Series

Exam Paper Generator

Online Exam Module