The angular frequency of a spring-block syste | vedclass

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

Question

(B) $1$. When the elevator is moving downwards at a constant speed $v_0$,the block is at rest relative to the elevator. When the elevator stops sudden

Vedclass · Accepted Answer

The initial phase of the block is $\pi$.

Vedclass · Answer

(B) $1$. When the elevator is moving downwards at a constant speed $v_0$,the block is at rest relative to the elevator. When the elevator stops suddenly,the block continues to move downwards with an initial velocity $v_0$ relative to the ground.$2$. The equilibrium position of the spring-block system remains unchanged because the gravitational force and spring force are balanced. The block now has an initial velocity $v_0$ at the equilibrium position.$3$. The amplitude $A$ is given by $v_{max} = A\omega_0$,so $A = \frac{v_0}{\omega_0}$. Thus,option $A$ is correct.$4$. Since the block starts from the equilibrium position moving in the positive (downward) direction,the equation of motion is $x(t) = A \sin(\omega_0 t) = \frac{v_0}{\omega_0} \sin(\omega_0 t)$. Thus,option $C$ is correct.$5$. The maximum speed in $SHM$ is $v_{max} = A\omega_0 = \frac{v_0}{\omega_0} \cdot \omega_0 = v_0$. Thus,option $D$ is correct.$6$. The initial phase $\phi$ for $x(t) = A \sin(\omega_0 t + \phi)$ is $0$ because at $t=0$,$x=0$ and $v > 0$. Therefore,the statement that the initial phase is $\pi$ is incorrect.

Similar Questions

On a smooth inclined plane,a mass $M$ is attached between two massless springs of force constant $k$ each,as shown in the figure. The other ends of the springs are fixed to firm supports. The period of oscillation of the mass $M$ is

Springs of spring constants $K, 2K, 4K, 8K, \dots$ are connected in series. $A$ mass of $40 \, g$ is attached to the lower end of the last spring and the system is allowed to vibrate. What is the time period of oscillation in seconds? (Given $K = 2 \, N/cm$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module