Frequency and Period of SHM - AP Physics C: Mechanics
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Calculate the period: $f = 5$ Hz.
Calculate the period: $f = 5$ Hz.
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$T = 0.2$ s. Use $T = \frac{1}{f} = \frac{1}{5}$ s.
$T = 0.2$ s. Use $T = \frac{1}{f} = \frac{1}{5}$ s.
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Identify the variable $k$ in the mass-spring system formula.
Identify the variable $k$ in the mass-spring system formula.
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Spring constant (N/m). $k$ measures the spring's resistance to deformation.
Spring constant (N/m). $k$ measures the spring's resistance to deformation.
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State the formula for the period of a mass-spring system.
State the formula for the period of a mass-spring system.
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$T = 2\pi\sqrt{\frac{m}{k}}$. Period increases with mass and decreases with spring stiffness.
$T = 2\pi\sqrt{\frac{m}{k}}$. Period increases with mass and decreases with spring stiffness.
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State the formula for the period of a simple pendulum.
State the formula for the period of a simple pendulum.
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$T = 2\pi\sqrt{\frac{L}{g}}$. Period depends only on length and gravity, not mass or amplitude.
$T = 2\pi\sqrt{\frac{L}{g}}$. Period depends only on length and gravity, not mass or amplitude.
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What is the unit of frequency in the SI system?
What is the unit of frequency in the SI system?
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Hertz (Hz). One hertz equals one cycle per second.
Hertz (Hz). One hertz equals one cycle per second.
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What type of motion does SHM describe?
What type of motion does SHM describe?
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Simple Harmonic Motion. Motion that repeats with constant frequency and amplitude.
Simple Harmonic Motion. Motion that repeats with constant frequency and amplitude.
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What is the angular frequency in terms of frequency?
What is the angular frequency in terms of frequency?
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$\omega = 2\pi f$. Angular frequency is $2\pi$ times the regular frequency.
$\omega = 2\pi f$. Angular frequency is $2\pi$ times the regular frequency.
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Convert $f = 10$ Hz to period.
Convert $f = 10$ Hz to period.
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$T = 0.1$ s. Use $T = \frac{1}{f} = \frac{1}{10}$ s.
$T = 0.1$ s. Use $T = \frac{1}{f} = \frac{1}{10}$ s.
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What is the unit of frequency in the SI system?
What is the unit of frequency in the SI system?
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Hertz (Hz). One hertz equals one cycle per second.
Hertz (Hz). One hertz equals one cycle per second.
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Determine period change: $L$ increases by 9 times.
Determine period change: $L$ increases by 9 times.
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Period triples. Period increases by $\sqrt{9} = 3$.
Period triples. Period increases by $\sqrt{9} = 3$.
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Calculate the frequency: $T = 0.5$ s.
Calculate the frequency: $T = 0.5$ s.
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$f = 2$ Hz. Use $f = \frac{1}{T} = \frac{1}{0.5}$ Hz.
$f = 2$ Hz. Use $f = \frac{1}{T} = \frac{1}{0.5}$ Hz.
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Calculate the period: $f = 5$ Hz.
Calculate the period: $f = 5$ Hz.
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$T = 0.2$ s. Use $T = \frac{1}{f} = \frac{1}{5}$ s.
$T = 0.2$ s. Use $T = \frac{1}{f} = \frac{1}{5}$ s.
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What happens to frequency if pendulum length is halved?
What happens to frequency if pendulum length is halved?
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Frequency increases by factor of $\sqrt{2}$. Frequency scales inversely with square root of length.
Frequency increases by factor of $\sqrt{2}$. Frequency scales inversely with square root of length.
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What happens to period if mass in mass-spring is halved?
What happens to period if mass in mass-spring is halved?
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Period decreases by factor of $\sqrt{2}$. Period scales with square root of mass.
Period decreases by factor of $\sqrt{2}$. Period scales with square root of mass.
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Find frequency of pendulum: $L = 1$ m, $g = 9.8$ m/s².
Find frequency of pendulum: $L = 1$ m, $g = 9.8$ m/s².
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$f \approx 0.5$ Hz. Use $f = \frac{1}{2\pi}\sqrt{\frac{g}{L}}$ with given values.
$f \approx 0.5$ Hz. Use $f = \frac{1}{2\pi}\sqrt{\frac{g}{L}}$ with given values.
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Find period of spring-mass: $m = 0.5$ kg, $k = 200$ N/m.
Find period of spring-mass: $m = 0.5$ kg, $k = 200$ N/m.
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$T \approx 0.314$ s. Use $T = 2\pi\sqrt{\frac{m}{k}}$ with given values.
$T \approx 0.314$ s. Use $T = 2\pi\sqrt{\frac{m}{k}}$ with given values.
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Find frequency for $T = 4$ seconds.
Find frequency for $T = 4$ seconds.
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$f = 0.25$ Hz. Direct application of $f = \frac{1}{T}$.
$f = 0.25$ Hz. Direct application of $f = \frac{1}{T}$.
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What is the relationship between amplitude and period?
What is the relationship between amplitude and period?
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No effect. SHM period depends only on system parameters, not amplitude.
No effect. SHM period depends only on system parameters, not amplitude.
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Describe the relationship between period and mass in SHM.
Describe the relationship between period and mass in SHM.
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Period increases with mass. From $T = 2\pi\sqrt{\frac{m}{k}}$, period increases with mass.
Period increases with mass. From $T = 2\pi\sqrt{\frac{m}{k}}$, period increases with mass.
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Calculate period: $L = 4$ m, $g = 9.8$ m/s².
Calculate period: $L = 4$ m, $g = 9.8$ m/s².
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$T \approx 4.01$ s. Use pendulum formula with $L = 4$ m and $g = 9.8$ m/s².
$T \approx 4.01$ s. Use pendulum formula with $L = 4$ m and $g = 9.8$ m/s².
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What is the frequency of a system with $T = 8$ s?
What is the frequency of a system with $T = 8$ s?
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$f = 0.125$ Hz. Apply $f = \frac{1}{T} = \frac{1}{8}$ Hz.
$f = 0.125$ Hz. Apply $f = \frac{1}{T} = \frac{1}{8}$ Hz.
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Calculate: $\frac{1}{T}$ for $T = 2$ s.
Calculate: $\frac{1}{T}$ for $T = 2$ s.
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$f = 0.5$ Hz. Direct calculation using $f = \frac{1}{T}$.
$f = 0.5$ Hz. Direct calculation using $f = \frac{1}{T}$.
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Find period change: $k$ is increased by 16 times.
Find period change: $k$ is increased by 16 times.
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Period is quartered. Period scales as $\frac{1}{\sqrt{k}}$, so $\frac{1}{\sqrt{16}} = \frac{1}{4}$.
Period is quartered. Period scales as $\frac{1}{\sqrt{k}}$, so $\frac{1}{\sqrt{16}} = \frac{1}{4}$.
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Convert $f = 10$ Hz to period.
Convert $f = 10$ Hz to period.
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$T = 0.1$ s. Use $T = \frac{1}{f} = \frac{1}{10}$ s.
$T = 0.1$ s. Use $T = \frac{1}{f} = \frac{1}{10}$ s.
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Determine frequency for $T = 0.1$ s.
Determine frequency for $T = 0.1$ s.
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$f = 10$ Hz. Use $f = \frac{1}{T} = \frac{1}{0.1}$ Hz.
$f = 10$ Hz. Use $f = \frac{1}{T} = \frac{1}{0.1}$ Hz.
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Calculate period for $f = 0.25$ Hz.
Calculate period for $f = 0.25$ Hz.
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$T = 4$ s. Apply $T = \frac{1}{f} = \frac{1}{0.25}$ s.
$T = 4$ s. Apply $T = \frac{1}{f} = \frac{1}{0.25}$ s.
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Find period: $m = 2$ kg, $k = 50$ N/m.
Find period: $m = 2$ kg, $k = 50$ N/m.
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$T \approx 1.26$ s. Use $T = 2\pi\sqrt{\frac{2}{50}} = 2\pi\sqrt{0.04}$ s.
$T \approx 1.26$ s. Use $T = 2\pi\sqrt{\frac{2}{50}} = 2\pi\sqrt{0.04}$ s.
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Find frequency: $m = 1$ kg, $k = 100$ N/m.
Find frequency: $m = 1$ kg, $k = 100$ N/m.
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$f \approx 0.5$ Hz. Use $f = \frac{1}{2\pi}\sqrt{\frac{k}{m}} = \frac{1}{2\pi}\sqrt{100}$ Hz.
$f \approx 0.5$ Hz. Use $f = \frac{1}{2\pi}\sqrt{\frac{k}{m}} = \frac{1}{2\pi}\sqrt{100}$ Hz.
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Predict period change: $L$ doubles.
Predict period change: $L$ doubles.
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Period increases by factor of $\sqrt{2}$. Period increases by $\sqrt{2}$ when length doubles.
Period increases by factor of $\sqrt{2}$. Period increases by $\sqrt{2}$ when length doubles.
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Predict frequency change: $k$ doubles.
Predict frequency change: $k$ doubles.
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Frequency increases by factor of $\sqrt{2}$. Frequency increases by $\sqrt{2}$ when $k$ doubles.
Frequency increases by factor of $\sqrt{2}$. Frequency increases by $\sqrt{2}$ when $k$ doubles.
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