Oscillation

Question 1

define restoring force

Answer 1

force that acts to return an object to its equilibrium position

Question 2

define simple harmonic motion

Answer 2

restoring force is directly proportional to displacement and in opposite direction

Question 3

at what displacement points, is velocity at a maximum and minimum?

Answer 3

velocity is zero when displacement in maximum

velocity is maximum when displacement in zero

Question 4

in terms of displacement, when is acceleration at it’s maximum and zero?

Answer 4

acceleration is maximum when displacement is maximum

acceleration is zero when displacement is zero

Question 5

what is the total energy in a free oscillation comprised of?

Answer 5

sum of potential energy and kinetic energy (total energy is constant throughout whole oscillation)

Question 6

what is total potential energy for a mass oscillating on a spring comprised of?

Answer 6

elastic strain energy, maximum at bottom, and gravitational potential energy, maximum at top

Question 7

calculate maximum kinetic energy of a mass of m attached to a spring with spring constant k that pulls spring down by x - it is pulled down a further e meters then released

Answer 7

1. initial elastic energy stored in spring (before being pulled down) = 1/2 • k • x^2
2. elastic energy stored after being pulled further = 1/2 • k • (x + e)^2
3. mass released and as moves through equilibrium position, therefore elastic energy decreases from 1/2k(x+e)^2 to 1/2kx^2 as gravitational potential energy increases by =
   m • g • e
4. kinetic energy = loss in elastic - gain in potential = [1/2k(x+e)^2 - 1/2kx^2] - mge

Question 8

define damping

Answer 8

removal of energy from an oscillating system (due to a resistive force acting in opposite direction to motion of oscillating object)

Question 9

describe difference between critically damped, heavily damped and under-damped

Answer 9

• critically damped: equilibrium attained in minimum time (ideal state for mechanical systems as prevents vibration damage)
• heavily damped: system takes too long to reach equilibrium position
• under-damped: unnecessary and possibly damaging vibrations

Question 10

define natural frequency

Answer 10

frequency at which a vibrating object undergoes free vibrations

Question 11

define forced oscillation

Answer 11

an oscillation imposed upon a system by an external energy source therefore forced to oscillate at frequency of external force = driving frequency

Question 12

define resonance and explain how it can occur

Answer 12

resonance: large amplitude vibrations, caused by driving frequency = natural frequency as means energy transferred to oscillator at maximum efficiency therefore amplitude increases

Question 13

at what point does amplitude of an oscillating system undergoing resonance stop increasing?

Answer 13

when energy supplied by driving frequency = energy lost by damping

Question 14

what are the advantages and disadvantages of resonance?

Answer 14

advantages: musical instruments, microwave cooker, MRI scanning
disadvantages: large amplitude vibrations can cause buildings/ bridges to shatter

Question 15

define resonant frequency and describe how it can be determined

Answer 15

resonant frequency: frequency at which resonance occurs

determined by connecting a clamped plastic rod to a signal generator + adjusting frequency until largest amplitude of oscillation found

Question 16

how does damping effect largest value of maximum amplitude, resonant frequency and sharpness of resonance curve?

Answer 16

decreases

Question 17

why do washing machines often have large blocks of concrete bolted to casing?

Answer 17

concrete increases mass of vibrating system which lowers its natural frequency so resonance doesn’t occur at motors normal running speed range

Question 18

when should x = sin(wt) be used and when should x = cos(wt) be used?

Answer 18

when x = 0 at t = 0 use sin(wt) when x = maximum at t = 0 use cos(wt)

Question 19

if in one cycle, a total distance of x meters traveled, what is amplitude?

Answer 19

x/2 meters

Question 20

when combining two springs in parallel and in series, how is the spring constant affected?

Answer 20

in series = halves overall spring constant

in parallel = doubles overall spring constant

Question 21

describe energy transfers over the cycle of a pendulum

Answer 21

from maximum displacement, kinetic energy is zero and gravitational potential energy is maximum, at moved toward equilibrium position, ADDITIONAL gravitational potential energy converted to kinetic energy and it increases to a maximum at the equilibrium position

Question 22

how does a graph of gravitational potential energy vary with time

Answer 22

cosine squared

Question 23

what is the phase difference between a forced vibration and displacement of an oscillating body undergoing resonance?

Answer 23

pi / 2 - quarter of a cycle

Question 24

why is it better to place fiducial marker at equilibrium position than at extremes when trying to time time period?

Answer 24

amplitude constantly decreasing because of damping

Question 25

how do you calculate initial amplitude of oscillation?

Answer 25

amplitude = arc length = r0