# Unit 6: Simple Harmonic Motion

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Simple Harmonic Motion (SHM)

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### 20 Terms

1

Simple Harmonic Motion (SHM)

Type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and is directed towards it.

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2

Displacement

The distance of an object from its equilibrium position in Simple Harmonic Motion, given by x = A cos(ωt + φ).

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3

Velocity

The rate of change of displacement in Simple Harmonic Motion, given by v = -Aω sin(ωt + φ).

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4

Acceleration

The rate of change of velocity in Simple Harmonic Motion, given by a = -Aω^2 cos(ωt + φ).

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5

Energy in SHM

The total mechanical energy of a system undergoing SHM is constant and is the sum of kinetic and potential energy.

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6

Force in Simple Harmonic Motion

The force exerted by a spring in Simple Harmonic Motion, given by F = -kx, where k is the spring constant and x is the displacement.

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7

Amplitude

The maximum displacement of a particle from its equilibrium position in a wave.

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8

Period

The time it takes for one complete cycle of a wave to occur, denoted by T and measured in seconds (s).

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9

Frequency

The number of complete cycles of a wave that occur in one second, denoted by f and measured in Hertz (Hz).

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10

Formula for Period of a Pendulum

T=2π√(L/g)

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11

Formula for Period of a Spring

T=2π√(m/k)

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12

Formula for Total Energy in Simple Harmonic Motion

E = ½kA²

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13

Formula for Kinetic Energy in Simple Harmonic Motion

K = ½mv²

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14

Formula for Potential Energy in Simple Harmonic Motion

U = ½kx²

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15

Where is velocity is maximum?

At the equilibrium position.

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16

Where is velocity is minimum?

At the extreme positions.

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17

What is the shape of a graph of simple harmonic motion relative to time?

Sinusoidal curve.

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18

What is the spring constant?

Denoted as “k”. It tells us how strong the spring is, with a greater k being a stiffer spring.

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19

How are frequency and period related?

Inversely related. For example, T = 1/f.

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20

What can amplitude demonstrate about an object with simple harmonic motion?

The intensity and energy level of the object.

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