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4 parts
1.1

T=2πlgT = 2\pi \sqrt{\dfrac{l}{g}}

1.2

9.8 m/s29.8 \, \mathrm{m/s^2}

1.3

2.0 s2.0 \, \mathrm{s}

1.4

1.4 s1.4 \, \mathrm{s}

Step-by-step solution

4 steps

Part 1.1· 1 step

Sihinu ifọ ti akọkọ ti ìsalẹ̀ (State the formula for the period of oscillation)

  1. The period $ T $ of a simple pendulum undergoing small oscillations is given by

    T=2πlgT = 2\pi \sqrt{\frac{l}{g}}

    where ll is the length of the string in meters (m) and gg is the acceleration due to gravity in meters per second squared (m/s2\mathrm{m/s^2}).

    T = 2\pi \sqrt{\dfrac{l}{g}}

Part 1.2

9.8 m/s29.8 \, \mathrm{m/s^2}

Nika ìyè g ní South Africa (Value of $ g $ in South Africa)

  1. The acceleration due to gravity in South Africa is approximately

    g≈9.8 m/s2g \approx 9.8 \, \mathrm{m/s^2}

    9.8 , m/s^2

Part 1.3

2.0 s2.0 \, \mathrm{s}

Ṣe ìṣirò ìyè akọkọ fún pendulum tí ó ni gigùn 1 m (Calculate period for length 1 m)

  1. Use the formula for the period

    T=2πlgT = 2\pi \sqrt{\frac{l}{g}}

    Substitute l=1 ml = 1 \, \mathrm{m} and g=9.8 m/s2g = 9.8 \, \mathrm{m/s^2}:

    T=2π19.8T = 2\pi \sqrt{\frac{1}{9.8}}

    Calculate the fraction:

    19.8≈0.1020\frac{1}{9.8} \approx 0.1020

    Take the square root:

    0.1020≈0.3194\sqrt{0.1020} \approx 0.3194

    Multiply by 2π2\pi (using π≈3.142\pi \approx 3.142):

    2×3.142×0.3194≈6.284×0.3194≈2.01 s≈2.0 s2 \times 3.142 \times 0.3194 \approx 6.284 \times 0.3194 \approx 2.01 \, \mathrm{s} \approx 2.0 \, \mathrm{s}

    2.0 , s

Part 1.4

1.4 s1.4 \, \mathrm{s}

Ìṣirò fún gigùn mìíràn (Assuming length 0.5 m as common follow-up; adjust if diagram specifies)

  1. Use the formula

    T=2πlgT = 2\pi \sqrt{\frac{l}{g}}

    Substitute l=0.5 ml = 0.5 \, \mathrm{m}, g=9.8 m/s2g = 9.8 \, \mathrm{m/s^2}:

    T=2π0.59.8T = 2\pi \sqrt{\frac{0.5}{9.8}}

    Calculate the fraction:

    0.59.8≈0.05102\frac{0.5}{9.8} \approx 0.05102

    Take the square root:

    0.05102≈0.2259\sqrt{0.05102} \approx 0.2259

    Multiply by 2π2\pi:

    2×3.142×0.2259≈6.284×0.2259≈1.42 s2 \times 3.142 \times 0.2259 \approx 6.284 \times 0.2259 \approx 1.42 \, \mathrm{s}

    1.4 , s

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