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High School Physics : Using Pendulum Equations

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Example Questions

Example Question #1 : Using Pendulum Equations

A 1kg mass on a pendulum is dropped from rest. It is observed that the period of the oscillation is . What is the length of the string?

$\small g=-9.8\frac{m}{s^2}$

Possible Answers:

3.33m

8.94m

0.92m

9.99m

0.955m

Correct answer:

8.94m

Explanation:

The equation for the period of a pendulum is $T=2\pi\sqrt{\frac{L}{g}}$ .

The mass on the pendulum is irrelevant when calculating the relationship between period and string length, as the only variables in the equation are the length of the string and gravity.

Since we are given the period and the constant for gravity, we can solve for the string length.

$6s=2\pi\sqrt{\frac{l}{9.8\frac{m}{s^2}}}$

$\frac{6s}{2\pi}=\sqrt{\frac{l}{9.8\frac{m}{s^2}}}$

$0.955s=\sqrt{\frac{l}{9.8\frac{m}{s^2}}}$

$(0.955s)^2=(\sqrt{\frac{l}{9.8\frac{m}{s^2}}})^2$

$0.912s^2=\frac{l}{9.8\frac{m}{s^2}}$

$0.912s^2* 9.8\frac{m}{s^2}=l$

8.94m=l

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Example Question #2 : Using Pendulum Equations

A 5kg mass on a pendulum is dropped from rest. If the length of the string is 20m , what is the period of oscillation?

$\small g=-9.8\frac{m}{s^2}$

Possible Answers:

4.49s

9.8s

19.8s

8.98s

20s

Correct answer:

8.98s

Explanation:

The equation for the period of a pendulum is $T=2\pi\sqrt{\frac{L}{g}}$ .

The mass on the pendulum is irrelevant when calculating the relationship between period and string length, as the only variables in the equation are the length of the string and gravity.

Since we are given the string length and the constant for gravity, we can solve for the period.

$T=2\pi\sqrt{\frac{20m}{9.8\frac{m}{s^2}}}$

$T=2\pi\sqrt{2.04s^2}$

$T=2\pi( 1.43s)$

T=8.98s

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Example Question #2 : Using Pendulum Equations

A pendulum of length is attached to a mass of 8kg . As it swings back and forth, what is the period?

$\small g=-9.8\frac{m}{s^2}$

Possible Answers:

5.68s

1.79s

1.14s

3.48s

11.36s

Correct answer:

3.48s

Explanation:

The formula for period of a pendulum is:

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

We are given the length of the string and the acceleration due to gravity. We are also given the mass, but this information is irrelevant; period is independent of mass.

Use the given values to solve for the period.

$T=2\pi\sqrt{\frac{3m}{9.8\frac{m}{s^2}}}$

$T=2\pi \sqrt{0.31s^2}$

$T=2\pi* 0.55s$

T=3.48s

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High School Physics : Using Pendulum Equations

Study concepts, example questions & explanations for High School Physics

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Example Question #1 : Using Pendulum Equations

Example Question #2 : Using Pendulum Equations

Example Question #2 : Using Pendulum Equations

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