Simple Harmonic Oscillations

Question 1

What is elasticity?

Answer 1

Elastic objects change shape when a force is applied to them however have the ability of to resume its normal shape after being stretched or compressed

Question 2

What is the elastic limit?

Answer 2

If the applied force is too great its shape may be permanently strained, this happens when it exceeds its elastic limit.

Question 3

What is the restoring force?

Answer 3

The force that always pushes or pulls the object towards the equilibrium position, when stretched

Question 4

What is Hooke’s Law?

Answer 4

The extension of an elastic object is directly proportional to the force applied to it. It takes about twice as much force to stretch a spring twice as far.
(F = - k.x)
Force (F) is measured in newtons (N)
Spring constant (k) is measured in newtons per metre (N/m) - how stiff the spring is.
Extension (e), or increase in length, is measured in metres (m)

Question 5

What is the extension of the spring?

Answer 5

When an elastic object is stretched, the increased length is called its extension (a strain applied).

Question 6

Why in hooke’s law, is the spring constant negative?

Answer 6

The force exerted by the spring is always in the opposite direction to the stretch (or compression) of the spring.

Question 7

What sort of an object would be a valid case for Hooke’s Law?

Answer 7

An object on an ideal spring that undergoes a small displacement from its equilibrium position is a valid case for Hooke’s law

Question 8

What is simple harmonic motion?

Answer 8

When an object oscillates (moves) back and forth over the same path in a repeated motion.

Question 9

How do you know if a body is in simple harmonic motion?

Answer 9

A body is in simple harmonic motion if

• Its acceleration is directly proportional to its distance from a fixed point on its path
• Its acceleration is always directed towards that point

Question 10

When does simple harmonic motion occur?

Answer 10

When the net force along the direction of motion obeys Hooke’s law – when the net force is proportional to the displacement from the equilibrium point and is always directed toward the equilibrium point.

Question 11

What is a cycle/osscilation?

Answer 11

It is the movement from A to B and back again to A.

Question 12

What is the period/periodic time?

Answer 12

Time taken for one complete oscillation (one position to other position) (T = 1/f) (T = 2Π / ω)

Question 13

What is the Frequency?

Answer 13

is the number of oscillations per second, one cycle per second is called one hertz (Hz) ( f = 1/T) (f =ω2π)

Question 14

What is the amplitude?

Answer 14

is the greatest displacement/ maximum distance of the object from its equilibrium position.

Question 15

To stretch/compress/extend a spring, what must be done?

Answer 15

an external force must have been applied to the object to overcome the spring’s restoring force, Work must be done by this external force.

Question 16

How do you find the work done on a spring?

Answer 16

1/2kx^2
x= size of displacement (cm)
k= spring’s constant

Question 17

What is k?

Answer 17

Spring constant k is specific for each spring.

Question 18

What is the equation which relates the spring constant, weight and displacement, and how is the spring constant found?

Answer 18

W = kx. (spring constant k is the slope of the straight line W versus x plot)

Question 19

What is work also equal to?

Answer 19

Potential energy

Question 20

As a body moved with SHM, how does the energy change?

Answer 20

its energy continually changes from potential to kinetic and back to potential.

Question 21

What is angular frequency?

Answer 21

angular displacement per unit time

ω =2ΠF (frequency in hertz can be converted to an angular frequency by multiplying it by 2π.)

Question 22

What is a simple pendulum?

Answer 22

A simple pendulum consists of a small mass called a bob attached to a fixed point by a massless spring

Question 23

When can a simple pendulum move with SHM?

Answer 23

If the angle is not more than 5 degrees

Question 24

How do you find total energy for an undamped oscillator?

Answer 24

sum of its kinetic energy (KE) and potential energy

(PE), which is constant at E = 1/2kA^2 A=amplitude

Question 25

Are the equations of linear motion with
constant acceleration valid in physics
problems of simple harmonic oscillation?
v = v0 + at 
s = v0t + 1/2 at^2
v^2 = v0^2 + 2as
A. Yes
B. No
C. In some
cases

Answer 25

B. No, Because the spring force depends on the distance x , the acceleration is not constant.

Question 26

The amplitude of a system moving in simple
harmonic motion is increased by a factor of 3.
Determine the change in
(a) the total energy,
(b) the maximum speed,
(c) the period, and
(d) the angular frequency.

Answer 26

a) E = ½ kA^2
A^2 = 3^2 = 9 times X9
b) Speed = 2πfA 
2πf(3) x3
c) same (no amplitude in equation)
d)same

Question 27

If the diving board takes 0.080 seconds to make one complete vibration, how many vibrations does it make each second?

(a) That is, if its period T is 0.080 sec, what is its frequency?
(b) What is the time required for one vibration of a guitar string that has a frequency of 264 Hz (middle C)?

Answer 27

a) 1/T = 1/.080 = 12.5

b) 1/264 = .0038 seconds

Question 28

How can the period of a simple pendulum be found?

Answer 28

period of such a pendulum can be approximated by:

T = 2π√L/ g

Question 29

When the term ‘‘vibration’’ is used, what does it mean?

Answer 29

The term vibration is sometimes used more narrowly to

mean a mechanical oscillation.

Question 30

What is the angular displacement defined by?

Answer 30

S/r
S= arc length
r = radius

Question 31

What is the angular velocity defined by?

Answer 31

how quickly an object moves through an angle. ω = v/r

Question 32

What is the angular acceleration equation?

Answer 32

a = a1/r

Question 33

What is the momentum?

Answer 33

the quantity of motion that an object has, p =mv (m- mass, v - velocity)

Question 34

What is the angular momentum?

Answer 34

quantity of rotation of a body, L = Iω (I-inertia, ω = angular velocity)

Question 35

How to find kinetic energy of linear and rotational motion

Answer 35

linear : 1/2 mv^2

rotational : 1/2Iω^2

Question 36

What is the moment of inertia?

Answer 36

defined as the product of the mass times the distance

from the axis squared

Question 37

What is a torsional pendulum?

Answer 37

is an oscillator for which the restoring force is torsio

twisting of an object due to an applied torque). (τ, it is the equivalent of force for rotational motion

Question 38

The restoring force acting on a spring is not
proportional to …
A. the change of position
of the spring from its “natural” position
B. the length of the spring
C. the “stretch” of the spring
D. the displacement of the spring from its equilibrium position

Answer 38

B

Question 39

The period of oscillation of a bungee jumper is
not dependent on the …
A. amplitude of oscillation
B. mass of the person
C. cross-sectional area of the bungee rope
D. length of the bungee rope

Answer 39

not dependant on (A)
NOT B = Inc mass – slower
NOT C OR D = IT DOES

Question 40

As a person stands on the bathroom scales, the spring inside the scales compresses by 0.06 mm and the display reads “72 kg”.

(a) Explain how a spring can be used to measure various masses.
(b) Show that the spring constant is 1.18 x 10^6 N/m.

Answer 40

a) The displacement a spring is stretched for a given force or weight is first calibrated. Then you can use the spring scale to measure the weight of various objects.
X = .00006mm (converted to si units)
F = -k.X (force is acting in other direction)
F= m . g (mass x gravity)
72kg x 9.8 = 706
K = F/X
706/.00006 = 1.18 x 10^6

Question 41

a spring with spring constant k (200N/m) is stretched from x=0 to x=3d, where X=0 is the equilibrium position of the spring. During which interval is the largest
amount of energy required to stretch the spring?
A. From x=0 to x=d
B. From x=d to x=2d
C. From x=2d to x=3d
D. The energy required is the
same in all three intervals

Answer 41

C. From x=2d to x=3d

As x gets larger, potential energy gets larger (U = 1/2kx^2)

Question 42

A spring is pressed against a wall so that it is compressed by 25 cm. (i.e. it is 25 cm shorter than its equilibrium length. The spring is then released. The spring constant is k= 35 N m-1, and the spring weighs 50 g. What is the speed at which the spring leaves the wall?
(A) 66.14 m/s
(B) 6.61 m/s
(C) 6.61 x 10-2 m/s
(D) 4.34 m/s
(E) 1.09 J

Answer 42

(.25 is the amplitude)
The formula with the linear speed is not applicable in this problem!
The easiest way is to use the conservation of energy:
The potential energy is converted into kinetic energy,
You know the potential energy since you have the spring constant and you have the amplitude since young the compression by .25
½ k x^2 = ½ m v^2 and solve for v
1/2 35