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Mechanical Engineering University First Year > Periodic Motion > Flashcards

Periodic Motion Flashcards

1
Q

What’s the equation for vertical shm when the body’s at equilibrium?

A

F=k(deltaL)-mg

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2
Q

An object at the end of a spring is oscillating in SHM. If the amplitude is doubled how does it affect the period (T) and the objects max speed (v_max)?

A

T remains the same and v_max doubles

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3
Q

From the equation x(t)= Acos(wt+theta) which describes the position as a function of time. what do you do to get the equation for acceleration as a function of time?

A

Differentiate twice

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4
Q

From the equation x(t)= Acos(wt+theta) which describes the position as a function of time. what do you do to to get the equation of velocity as a function of time?

A

Differentiate once

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5
Q

What is conserved in SHM?

A

Mechanical energy
E=K+U
(1/2kA^2)=(1/2mv^2)+(1/2kx^2)

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6
Q

To double the total energy of a mass spring system oscillating in SHM, the amplitude must increase by a factor of…

A

sqrt (2)

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7
Q

What’s the equation for angular SHM?

A

T=-ktheta

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8
Q

A simple pendulum consists of a point mass suspended by a massless, unstretchable string.

If the mass is doubled while the length of the string remains the same, the period of the pendulum…

A

Remains unchanged

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9
Q

If I have a phase angle that is -ve in the equation x(t)=Acos(wt+theta), what direction does the graph move?

A

The right

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10
Q

What is k in F=-kx

A

Spring constant in N/m

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11
Q

What is A in x(t)=Acos(wt+theta)?

A

Amplitude - max magnitude of displacement from the equilibrium

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12
Q

A frictionless pendulum having a length L and mass M swings wit period T. If both L and M double, what’s the new period?

A

Sqrt(2)T

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13
Q

Equal masses, suspended by separate strings of equal length; String 1 and 2. 1 has a larger cross sectional area than the 2nd
Which wire will stretch the least?

A

1

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14
Q

If the period doubles the frequency is…

A

Halved

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15
Q

If an oscillating object takes 0.10seconds to complete one cycle what is the frequency and equation to obtain it?

A

f=1/T from the equation T=1/f and the frequency is 10Hz

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16
Q

If the frequency is 40Hz what is the period

A

With T=1/f the period is 0.025 seconds

17
Q

For a block connected to a spring on a horizontal plane. The kinetic energy of the block reaches its maximum when…

A

The displacement of the block is zero (at the equilibrium)

18
Q

For a block connected to a spring on a horizontal plane. If the kinetic energy of the block is increasing the block must be…

A

Moving towards the equilibrium

19
Q

When is the potential energy of a spring at a maximum?

A

Both when the spring is most compressed and when the spring is most stretched

20
Q

How does the frequency of oscillation depend on the mass of the weight

A

The frequency decreases as the mass increases

21
Q

How does the amplitude of a string affect the frequency?

A

It doesn’t, the frequency is independent of the amplitude

22
Q

On a pendulum with two strings (massless) with equal bob masses attached, with the 2nd string being twice as long. When let go at the same time and position. How much longer is the period (T) for the 2nd string?

A

Sqrt(2)•T longer

23
Q

On a pendulum what is the velocity when the mass is at its max amplitude?

A

0

24
Q

On a swinging pendulum when the mass is at its equilibrium what direction is the acceleration?

A

Directly up towards the turning point.

25
Q

True or false: the acceleration is never equal to 0 on a swinging pendulum in SHM

A

True

26
Q

With the pendulum swinging back and forth, how does the tension of the rope compare to the force of gravity when the angle is 0

A

The tension is greater than the force of gravity

27
Q

On a pendulum in SHM, at an angle of (+-)90deg from the turning point, what is the tension? Is it at its max or min?

A

Min being 0N

28
Q

How does the period of oscillation depend on the initial angle of the pendulum when released?

A

The period is longer when the initial angle is greater

29
Q

How does the period of the pendulum depend on the length?

A

A longer pendulum has a longer period

30
Q

How does the period of oscillation depend on the gravity?

A

The higher value of gravity the longer the period is

Mechanical Engineering University First Year (2 decks)

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