A clock with a pendulum made of steel has a period of 1.000 s at 20.0°C. The temperature is decreased to 4°C.
By how much does the period change? How much time does the clock gain or lose in one week?

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  1. The pendulum length gets shorter and the frequency of oscillation increases.

    Compute the new length using the coefficent of thermal expansion of steel, 13*10^-6 C^-1.

    Call it the new length L2 and the original length L1.

    L2/L1 = 1 -13*10^-6*16 = 0.99979

    The new period P2 gets multiplied by sqrt(L2/L1)
    P2 = 1.0000*0.999896 = 0.999896 s

    One week is 10,080 minutes or 6.04800*10^5 s

    The new number of oscillations in one week will be 6.04800*10^5/0.999896 = 6.04863*10^5

    63 seconds or about one minute will be gained by the clock.

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