Simple harmonic motion  Question and answer

Simple harmonic motion Question and answer  1
what is damped oscillation?
Answer: Damped oscillation is one in which the amplitude gradually decrease with time and finally come to stop or zero.

Simple harmonic motion Question and answer  2
Is a body moving with constant speed in a circular path undergoing acceleration?
Answer: No it not undergoing acceleration, because the association is rate of change velocity but here the velocity is constant

Simple harmonic motion Question and answer  3
A 10kg mass is suspended from the end of a spring and released. If the spring oscillates in simple harmonic motion with a speed of 0.5s, find the energy given to the 10 kg mass if the amplitude of the oscillation is 2cm.

${ { T=2\pi \sqrt { \frac { m }{ k } } } }$

Where m=mass suspended and k= elastic constant

${ { 0.5=2\pi \sqrt { \frac { 10 }{ k } } } }$

Squaring the both side we have

${ { 0.25=4{ \pi }^{ 2 }\frac { 10 }{ K } } }$

${ { { K=\frac { 4{ \pi }^{ 2 }\times 10 }{ 0.25 } =\quad 160{ \pi }^{ 2 } }Kg/{ s }^{ 2 } } }$

For energy use

${ { { \frac { 1 }{ 2 } K{ x }^{ 2 } } } }$

where x = the amplitude=2cm=0.02m

${ { { =0.5\times 160{ \pi }^{ 2 }\times 4\times { 10 }^{ -4 } }=0.03{ \pi }^{ 2 }J } }$

Simple harmonic motion Question and answer  4
3. State the formula used in calculating period in simple pendulum and in loaded spiral spring performing simple harmonic oscillation

${ { T=2\pi \sqrt { \frac { L }{ g } } } }$

${ { T=2\pi \sqrt { \frac { m }{ k } } } }$

Simple harmonic motion Question and answer 5
what is the condition of acceleration of body performing simple harmonic motion?
Answer: Acceleration of a body performing simple harmonic motion is directed toward the fixed point and proportional to the distance from the fixed point.

Simple harmonic motion Question and answer  6
The period of a simple pendulum x is 1.5s. What is the period of a simple pendulum y which makes 500 vibration in the time it takes x to make 400 vibrations?

?s =     500 vibration , this implies that

${ { { \frac { 400\quad \times 1.5 }{ 500 } }=1.2s } }$

Simple harmonic motion Question and answer 7
What is resonance?
Answer: Resonance is a phenomenon which occurs whenever a particular body or a system is set to oscillation at its own natural frequency as a result of impulses or signals received from some other system or body which is vibrating with the same frequency

Simple harmonic motion Question and answer  8
What is the relationship between period and frequency?
Answer: the relationship is that the period is reciprocal of frequency, that is
T =1/F or  F=1/T

Simple harmonic motion Question and answer  9
Name one example of resonance

Simple harmonic motion Question and answer 10
A pendulum has a period of 4.2s, Calculate length of the pendulum ( g=9.8m/S2)

${ { T=2\pi \sqrt { \frac { L }{ g } } } }$

Square both side

${ { { T }^{ 2 }={ 2 }^{ 2 }{ \pi }^{ 2 }\frac { L }{ g } } }$

Make L the subject of the formula

${ { { L=\frac { { T }^{ 2 }{ g } }{ { 2 }^{ 2 }{ \pi }^{ 2 } } }=\frac { { 4.2 }^{ 2 }\times 9.8 }{ 4\times { 3.142 }^{ 2 } } } }$

${ { \frac { 172.872 }{ 39.48 } =4.4m } }$

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