Lesson 25 questions – SHM
(
1
/20)….…..%.......
This question is about a mass-spring system.
Fig1.1 shows a mass attached to two springs. The mass moves along a horizontal tube
with one spring stretched and the other compressed. An arrow marked on the mass
indicates its position on a scale. Fig 1.1 shows the situation when mass is displaced
through a distance x from its equilibrium position. The mass is experiencing an
acceleration a in the direction shown. Fig 1.2 shows a graph of the magnitude of the
acceleration against the displacement x.
fig 1.1
fig1.2
ALL
a)
i)
State one feature from each fig 1.1 and fig 1.2 which shows that
the mass performs harmonic motion when released.
…1.1…… acceleration in opposite direction to displacement
…1.2……acceleration proportional to displacement
………………………………………………………………………………………………
………………………………………………………………………………………… (2)
MOST
ii)
Use data from fig 1.2 to show that the frequency of the simple harmonic
oscillations of the mass is about 5Hz.
a=-(2πf)2x
grad = -(2πf)2
1000 / 4π2= f2
25.33 = 5.03 ≈ 5Hz
(3)
b)
The mass-spring system of fig 1.1 can be used as a device to measure
acceleration, called an accelerometer. It is mounted on a rotating test rig, used to simulate
large g-forces for astronauts. Fig 1.3 shows the plan view of a long beam rotating about
its axis A with the astronaut seated at end B, facing towards A. The accelerometer is
parallel to the beam and is fixed under the seat 10m from A.
fig 1.3
ALL
i)
When the astronaut is rotating at a constant speed, the arrow
marked on the mass has a constant deflection. Explain why.
…………At constant angular speed there is a constant centripetal acceleration toward the
centre of the circle.………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………… (2)
ii)
Calculate the speed v of rotation of the astronaut when the
deflection is 50mm.
at 50mm a= 50 ms-2
r=10m
a=v2/r
500= v2
v = ……22.4…………. ms-1 (2)
2
A bored student (in a biology lesson) holds one end of a flexible plastic ruler
against the laboratory bench and flicks the other end, setting the ruler into oscillation. The
end of the ruler moves a total distance of 8.0cm as in the diagram and makes 28 complete
oscillations in 10s.
SOME
a)
What are the amplitude x0 and frequency f of the motion of the end of the ruler?
28 oscillations in 10 seconds
One osc.=10/28
1 oscillation = 0.357s
f=1/T
x0 = ………0.04…………….. m (1)
f = ………2.8…………….. Hz (1)
ALL
b)
Use x= x0cos2πft to produce a table of values of x and t for values:
t/s = 0, 0.04, 0.08, 0.12, 0.16, 0.20, 0.24, 0.28, 0.32, 0.36
t/s
x/m
0
0.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
0.36
0
0.03051
0.00653
-0.02054
-0.03787
-0.03722
-0.0189
0.00838
0.03169
0.03996
(4)
Draw a graph on the attached graph paper of x against t and use it to find the maximum
speed at the end of the ruler.
(4)
displacement/m
q2
0.05
0.04
0.03
0.02
0.01
0
-0.01 0
-0.02
-0.03
-0.04
-0.05
0.1
0.2
0.3
0.4
gradient =
0.7 (+- 0.05)
ms-1
time/s