Is there is any change in time period if it is done inside accelerating lift?

[vkash]

Homework Statement

Q1> there is a cube like jar of water kept at the surface of a lift which is moving with an acceleration of a in upward direction. jar is filled with water. There is a cubical block of wood floating on it's surface. It is slightly pressed and released. find the time period of the Simple harmonic motion.(viscosity of liquid is zero)

Q2> A spring is attached to ceiling in lift will it's time period(of oscillations) change with acceletation of life(I think no).

Q3>A pendulum is attached to ceiling will it's time period vary with acceleration.(I think yes T=2πsqrt(l/g))

After all i come to conclusion that "it is mixed one. I mean if it is inside a lift it may or may not have same time period as it had"

Homework Equations

Archimedes principle and Simple equations of SHM.

The Attempt at a Solution

let me say after slight push it's mean position is displaced by x₀.
After a distance x below x₀ net force acting on the wooden block is dAx(g+a).
here d is density A is base area of block and g is acceleration due to gravity.
F=dAx(g+a) =mω²x (m is mass of block)
from here T(time period)=2πdqrt(m/[dA(g+a)] ).

IF i am wrong somewhere then please alert me.

(recently updated to firefox 9. it is not responding to spelling mistake so if i have done any mistake then please ignore that)

thanks for reading...
waiting for ur valuable reply..

 

[BruceW]

I'm assuming the acceleration of the lift is meant to be constant with time? In this case, I think you have got all the answers correct :) One spelling mistake though - you've written dqrt, but I think you mean sqrt (i.e. square root).

 

[vkash]

I'm assuming the acceleration of the lift is meant to be constant with time? In this case, I think you have got all the answers correct :) One spelling mistake though - you've written dqrt, but I think you mean sqrt (i.e. square root).

thnaks BruceW for answering.
Finally the answer behind the book is wrong and i am correct.

 

[BruceW]

about question 1>, there is also the force of gravity on the wooden block. But you still have the right answer, because this only affects where the point of equilibrium is. Also, the amplitude of oscillation must be small enough that the block doesn't jump out of the water. As long as this is true, then you've got the right answer for the period.

Textbooks sometimes do have wrong answers (usually due to error when the person wrote it). They probably checked it through a few times, but a few mistakes always seem to slip through the net. It shows that you understand the material if you can spot the errors :)

 

[asteriatic]

I can provide a response to the content provided.

Firstly, in regards to Q1, the time period of the simple harmonic motion will indeed change if it is done inside an accelerating lift. This is because the acceleration of the lift will affect the forces acting on the cube of water and the block of wood, causing a change in their respective positions and therefore changing the time period of the SHM.

In Q2, the time period of the spring's oscillations will also change with the acceleration of the lift. This is because the acceleration will affect the tension in the spring, which is a key factor in determining the spring's time period.

Finally, in Q3, the time period of the pendulum will indeed vary with acceleration. This is due to the fact that the acceleration of the lift will affect the gravitational force acting on the pendulum, which is a key factor in determining its time period.

Overall, it is important to consider the external factors, such as acceleration, when determining the time period of oscillations or SHM in a given system.