A `100g` block is connected to a horizontal massless spring of force constant `25.6 N//m`. The block is free to oscillate on a horizontal fricationless surface. The block is displced by `3 cm` from the equilibrium position, and at `t = 0`, it si released from rest at `x = 0`, The position-time graph of motion of the block is shown in figure.
_S01_052_Q01.png)
Let us now make a slight change to the initial conditions. At `t = 0`, let the block be released from the same position with an initial velocity `v_(1) = 64 cm//s`. Position of the block as a function of time can be expressed as
A `100g` block is connected to a horizontal massless spring of force constant `25.6 N//m`. The block is free to oscillate on a horizontal fricationless surface. The block is displced by `3 cm` from the equilibrium position, and at `t = 0`, it si released from rest at `x = 0`, The position-time graph of motion of the block is shown in figure.
Let us now make a slight change to the initial conditions. At `t = 0`, let the block be released from the same position with an initial velocity `v_(1) = 64 cm//s`. Position of the block as a function of time can be expressed as
Let us now make a slight change to the initial conditions. At `t = 0`, let the block be released from the same position with an initial velocity `v_(1) = 64 cm//s`. Position of the block as a function of time can be expressed as
A
`x = 5 sin 16t`
B
`x = 5sin(16t+37^(@))`
C
`x = 5sin(16t-37^(@))`
D
`x=5cos(16t +37^(@))`
Text Solution
Verified by Experts
The correct Answer is:
B
Let `x = A sin(16t + phi) v = Aomega cos (16t + phi)` where `omega^(2) = (K)/(m) = (25.6)/(0.1) = 256 rArr omega = 16"rad"/"sec"`
At`t = 0, 3 = A sinphi` & `64 = Acosphi rArr tanphi = 3/4 rArr phi = 37^(@)` Also `A = 5 cm`
Therefore equation of SHM `x = 5 sin (16t + 37^(@))`
At`t = 0, 3 = A sinphi` & `64 = Acosphi rArr tanphi = 3/4 rArr phi = 37^(@)` Also `A = 5 cm`
Therefore equation of SHM `x = 5 sin (16t + 37^(@))`
Topper's Solved these Questions
Similar Questions
Explore conceptually related problems
A 100g block is connected to a horizontal massless spring of force constant 25.6 N//m . The block is free to oscillate on a horizontal fricationless surface. The block is displced by 3 cm from the equilibrium position, and at t = 0 , it si released from rest at x = 0 , The position-time graph of motion of the block is shown in figure. When the block is at position A on the graph, its
A 100 g block is connected to a horizontal massless spring of force constant 25.6(N)/(m) As shown in Fig. the block is free to oscillate on a horizontal frictionless surface. The block is displaced 3 cm from the equilibrium position and , at t=0 , it is released from rest at x=0 It executes simple harmonic motion with the postive x-direction indecated in Fig. The position time (x-t) graph of motion of the block is as shown in Fig. Q. When the block is at position A on the graph, its
A 100 g block is connected to a horizontal massless spring of force constant 25.6(N)/(m) As shown in Fig. the block is free to oscillate on a horizontal frictionless surface. The block is displaced 3 cm from the equilibrium position and , at t=0 , it is released from rest at x=0 It executes simple harmonic motion with the postive x-direction indecated in Fig. The position time (x-t) graph of motion of the block is as shown in Fig. Q. When the block is at position B on the graph its.
A 100 g block is connected to a horizontal massless spring of force constant 25.6(N)/(m) As shown in Fig. the block is free to oscillate on a horizontal frictionless surface. The block is displaced 3 cm from the equilibrium position and , at t=0 , it is released from rest at x=0 It executes simple harmonic motion with the postive x-direction indecated in Fig. The position time (x-t) graph of motion of the block is as shown in Fig. When the block is at position C on the graph, its
A 100 g block is connected to a horizontal massless spring of force constant 25.6(N)/(m) As shown in Fig. the block is free to oscillate on a horizontal frictionless surface. The block is displaced 3 cm from the equilibrium position and , at t=0 , it is released from rest at x=0 It executes simple harmonic motion with the postive x-direction indecated in Fig. The position time (x-t) graph of motion of the block is as shown in Fig. Position of the block as a function of time can now be expressed as
A 100 g block is connected to a horizontal massless spring of force constant 25.6(N)/(m) As shown in Fig. the block is free to oscillate on a horizontal frictionless surface. The block is displaced 3 cm from the equilibrium position and , at t=0 , it is released from rest at x=0 It executes simple harmonic motion with the postive x-direction indecated in Fig. The position time (x-t) graph of motion of the block is as shown in Fig. Velocity of the block as a function of time can be expressed as
A block of mass m is connected to another .block of mass M by a massless spring of spring constant k. A constant force f starts action as shown in figure, then:
A block of mass m is connected with two ideal pullies and a massless spring of spring constant K as shown in figure. The block is slightly displaced from its equilibrium position. If the time period of oscillation is mupisqrt(m/K) . Then find the value of mu .
Two blocks rest on a smooth horizontal surface. They are connected by a spring of force constant k. If the system is set into oscillation find its time period.
A block whose mass m is 680g is fastened to a spring whose spring constant k is 65N/m. The block is pulled a distance x=11cm from its equilibrium position at x=0 on a frictionless surface and released from rest at t= 0. What is the phase constant phi for the motion?