Question

6. The dynamic spring constant k (in N/m) determined using an oscillating vertical spring is directly related to:

- the reciprocal of the slope of a graph of period squared (in s2) as a function of total added mass (in kg)

- the slope of a graph of period squared (in s2) as a function of total added mass (in kg)    

- the reciprocal of the slope of a graph of period (in s) as a function of total added mass (in kg)

- the reciprocal of the slope of a graph of period squared (in s2) as a function of total added weight (in N)

7. Which of the following is true for an ideal simple pendulum?

- The frequency of the oscillatory motion that results when the bob is pulled over to a small amplitude depends on the effective length of the string and the local acceleration due to gravity.

- It consists of a simple mass attached to a friction-less pivot point by a string of negligible mass.   

- The motion is considered as simple harmonic motion if confined to small amplitude oscillations.

- All of the answers are correct.

8. The local acceleration of gravity determined using a simple pendulum is directly related to:

- the reciprocal of the slope of a graph of period squared (in s2) as a function of effective string length (in m)

- the reciprocal of the slope of a graph of period squared (in s2) as a function of effective string length (in cm)   

- the reciprocal of the slope of a graph of period (in s) as a function of effective string length (in m)

- the slope of a graph of period squared (in s2) as a function of effective string length (in m)

9. Students performing the simple pendulum experiment:

- should take care to ensure that the pendulum travels in arcs and not circles

- All of the answers are correct.   

- should keep in mind that the effective length of the string is the overall length from the point where the string attaches to the mount to the middle of the suspended mass

- should deflect the pendulum to an amplitude of about 15 degrees and release it

should NOT cut the string but instead make adjustments at one of the attachment points

Answer 1

(6) Angular frequency is related to spring constant k and mass m as given below

....................(1)

since = 2/T , where T is period of oscillation , above equation is written as

T2 = m ( 42 / k )

From above expression, we can conclude, spring constant k is related to reciprocal of the slope of graph drawn for square of time period (T2 ) as a function added mass to spring.

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(7) The frequency of the oscillatory motion that results when the bob is pulled over to a small amplitude depends on the effective length of the string and the local acceleration due to gravity.

- Above statement is TRUE

frequency f of oscillation is given by ,

where g is acceleration due to gravity and l is length of pendulam.

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It consists of a simple mass attached to a friction-less pivot point by a string of negligible mass.

Above statement is TRUE

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The motion is considered as simple harmonic motion if confined to small amplitude oscillations.

Above statement is TRUE

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Hence All of the answers are correct

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(8) Period of simple pendulam is given as

Hence we get ,

hence we conclude that acceleration due to gravity is related to the reciprocal of the slope of a graph of period squared (in s2) as a function of effective string length (in m)

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(9) All answers are correct