15.2 Springs and SHM

Question 1

Most springs that obey hooke’s law also obey what?

Answer 1

simple harmonic motion

Question 2

When a spring (with one fixed end and one that can be moved) is in equilibrium position what forces are acting on the movable block?

Answer 2

The reaction force and weight

Question 3

When a spring (with one fixed end and one that can be moved) is stretched what forces are acting on the movable block?

Answer 3

The reaction force,weight, force towrads equilibrium position. Although not a force the displacement is acting in the opposite direction.

Question 4

What do the 2 examples above assume?

Answer 4

The track is frictionless?

Question 5

What equation do we get when combining hooke’s law and newtons second law?

Answer 5

F=ma and F = kx 
ma = kx 
a = -k/m x  
when looking at a = -(omega)^2x 
we can see omega = square root m/k

Question 6

What equation is used to give the period of of shm of spring?

Answer 6

T = 2π(square root)m/k

Question 7

Is this equation used only for horizontally oscillating springs?

Answer 7

No, this equation can be used for vertically oscillating springs

Question 8

What does the spring need to obey to follow shm?

Answer 8

Hooke’s Law

Question 9

What is hooke’s law?

Answer 9

Extension is directly proportional to force applied.

Question 10

What needs to be met about the spring to follow this equation if it is oscillating vertically?

Answer 10

Must be light.

Question 11

What setup can we use to find the spring constant k using simple harmonic motion?

Answer 11

A workbench with a stand , which has a clamped string attached to a spring with masses. Below the spring there is a position sensor(can be replaced with a marker on ruler called the fiducial marker). Ruler is placed alongside the spring .

Question 12

How does this practical work?

Answer 12

1) Pull down the spring with the mass (this is the amplitude)
2) The masses oscillate with shm
3) The position sensor measures displacement over time
4) Create a displacement time graph and work out period (oscillations over time to get amount of oscillations per second)
5) Rearrange T = 2π(square root)m/k to get the k and substitute T and m.

Question 13

If this experiment was performed without a position sensor what would be the problem?

Answer 13

The displacement time graph wouldn’t be drawn very well

Question 14

What setup can we use to find the spring constant using hooke’s law?

Answer 14

Stand with a clamped ruler and spring with masses. Also a set square on the side

Question 15

How does this practical work?

Answer 15

1) A mass is suspended from a vertical spring
2) Use a set square to determine equilibrium position (this reduces parallax error)
3) Add mass
4) Record new h and calculate extension
5) Repeat to tabulate enough readings
6) Draw a graph of F against x, the graph should be straight line through the origin if hooke’s law is obeyed
gradient is the k (spring constant and essentially the stiffness)

Question 16

How is k changed if springs are placed next to each other and used in an experiment?

Answer 16

Multiplies k by the amount of springs placed parallel to each other

Question 17

How is k changed if springs are attatched to each other top to bottom(series)?

Answer 17

k is divided by the amount of springs

Question 18

Hence what is the equation for k in parallel and in series?

Answer 18

1/k = 1/k1 + 1/k2 in series
k = k1 + k2 in parallel
same as capacitors and opposite to resistance

Question 19

How does T change with mass?

Answer 19

Increases with mass (T^2 is proportional to m)

Question 20

How does T change with k (the spring constant )?

Answer 20

T^2 is proportional to 1/k hence decreases with k

Question 21

How does T change with amplitude?

Answer 21

It doesn’t change

Question 22

Do period and frequency depend on amplitude?

Answer 22

No, the time interval and hence frequency will not change