6.1 AP Physics C: Mechanics

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period for any SHM oscillator

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1

period for any SHM oscillator

<span>T=1f=2πω<span>T=\frac{1}{f}=\frac{2π}{ω}

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2

period for a spring system

<span>T=2πmk<span>T=2π\sqrt{\frac{m}{k}}

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3

period of a simple pendulum

<span>Tp=2πLg<span>T_p=2π\sqrt{\frac{L}{g}}

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4

period of a physical pendulum

<span>Tp=2πImgh<span>T_p=2π\sqrt{\frac{I}{mgh}}

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5

frequency

<span>f=1T=ω2π<span>f=\frac{1}{T}=\frac{ω}{2π}

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6

displacement

<span>x(t)=xmcos(ωt+φ)<span>x(t)=x_m*\cos{(ωt+φ)}

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7

velocity

<span>v(t)=ωxmsin(ωt+φ)<span>v(t)=-ω*x_m*\sin{(ωt+φ)}

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8

acceleration

<span>a(t)=ω2x(t)<span>a(t)=-ω^2*x(t)

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9

angular frequency for any SHM oscillator

<span>ω=2πT=2πf<span>ω=\frac{2π}{T}=2πf

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10

angular frequency of a spring system

<span>ω=km<span>ω=\sqrt{\frac{k}{m}}

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11

velocity amplitude

<span>vm=ωxm<span>v_m=ωx_m

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12

acceleration amplitude

<span>am=ω2xm<span>a_m=ω^2x_m

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13

spring force

<span>F=(mω2)x=kx<span>F=-(mω^2)x=-kx

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14

conservation of energy

<span>E=U(t)+K(t)<span>E=U(t)+K(t)

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