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Frequency and Period of SHM

AP Physics 1· difficulty 4/5

m k

A mass m=0.5 kgm = 0.5\,\text{kg} attached to a horizontal spring oscillates with amplitude 0.10 m0.10\,\text{m} and maximum speed 2.0 m/s2.0\,\text{m/s}. What is the spring constant kk and the period TT?

  • A

    k=400 N/mk = 400\,\text{N/m}, T≈0.22 sT \approx 0.22\,\text{s}

  • B

    k=200 N/mk = 200\,\text{N/m}, T≈0.31 sT \approx 0.31\,\text{s}

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  • C

    k=50 N/mk = 50\,\text{N/m}, T≈0.63 sT \approx 0.63\,\text{s}

  • D

    k=100 N/mk = 100\,\text{N/m}, T≈0.45 sT \approx 0.45\,\text{s}

Explanation

From vmax⁡=Aωv_{\max} = A\omega, ω=2.0/0.10=20 rad/s\omega = 2.0/0.10 = 20\,\text{rad/s}. Then k=mω2=0.5⋅400=200 N/mk = m\omega^2 = 0.5\cdot 400 = 200\,\text{N/m}, and T=2π/ω≈0.314 sT = 2\pi/\omega \approx 0.314\,\text{s}.

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