..
If mass attached to a spring is made four times, maximum velocity becomes
1
(A) Half
(B) Twice
(C) 1/4 times
(D) 4 times
*explain with solution*
Answers
Answer:
University Physics Volume 1
15 Oscillations
15.2 Energy in Simple Harmonic Motion
LEARNING OBJECTIVES
By the end of this section, you will be able to:
Describe the energy conservation of the system of a mass and a spring
Explain the concepts of stable and unstable equilibrium points
To produce a deformation in an object, we must do work. That is, whether you pluck a guitar string or compress a car’s shock absorber, a force must be exerted through a distance. If the only result is deformation, and no work goes into thermal, sound, or kinetic energy, then all the work is initially stored in the deformed object as some form of potential energy.
Consider the example of a block attached to a spring on a frictionless table, oscillating in SHM. The force of the spring is a conservative force (which you studied in the chapter on potential energy and conservation of energy), and we can define a potential energy for it. This potential energy is the energy stored in the spring when the spring is extended or compressed. In this case, the block oscillates in one dimension with the force of the spring acting parallel to the motion:
W
=
x
f
∫
x
i
F
x
d
x
=
x
f
∫
x
i
−
k
x
d
x
=
[
−
1
2
k
x
2
]
x
f
x
i
=
−
[
1
2
k
x
2
f
−
1
2
k
x
2
i
]
=
−
[
U
f
−
U
i
]
=
−
Δ
U
.
When considering the energy stored in a spring, the equilibrium position, marked as
x
i
=
0.00
m,
is the position at which the energy stored in the spring is equal to zero. When the spring is stretched or compressed a distance x, the potential energy stored in the spring is
U
=
1
2
k
x
2
.
Energy and the Simple Harmonic Oscillator
To study the energy of a simple harmonic oscillator, we need to consider all the forms of energy. Consider the example of a block attached to a spring, placed on a frictionless surface, oscillating in SHM. The potential energy stored in the deformation of the spring is
U
=
1
2
k
x
2
.
Answer:
If mass attached to a spring is made four times, maximum velocity becomes Twice.
Explanation:
- The mass that is linked to the spring has no bearing on its force constant. As a result, it remains unchanged by the attached mass.
- The maximum velocity doubles when the amplitude is doubled. (iii) The acceleration at the mean position is zero and unaffected by the vibration's amplitude. As a result, there is no change in the acceleration at mean position.
maximum speed of a spring as an example
With a maximum velocity of 1.5 m/s, it passes through the vertical spring's equilibrium position. Its velocity in terms of time is given by
v(t) = -ωAsin(ωt + φ).
A spring's velocity is impacted by mass.
- According to Newton's second law, F = ma, a stiffer or more powerful spring produces more force.
- That entails a higher acceleration for a given mass, which causes the mass to travel more quickly and, as a result, complete its motion more quickly or in a shorter amount of time.
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