Ubude bempendulo ewangcwisiwe ngokukhulu mabube ngamagama angama–340–390. - NSC IsiXhosa HL - Question 18 - 2018 - Paper 2

To find the angular displacement of the pendulum, we begin by determining the relationship between the total time period and the linear displacement. The formula to calculate the length of the pendulum based on its time period is given by:

$T = 2\pi \sqrt{\frac{L}{g}}$

Where:

• $T$ = time period
• $L$ = length of the pendulum
• $g$ = acceleration due to gravity (approximately $9.81 \ m/s^2$)

Rearranging the equation to solve for $L$, we have:

$L = \frac{g T^2}{4\pi^2}$

Using the provided values for the angular measurements (340–390 degrees), we can convert these angles into radians, where:

$\text{Radians} = \frac{\text{Degrees} \times \pi}{180}$

Thus,

$340 \text{ degrees} = \frac{340 \times \pi}{180} \approx 5.934 \text{ radians}$ $390 \text{ degrees} = \frac{390 \times \pi}{180} \approx 6.806 \text{ radians}$

Next, apply the angular displacement formula to compute the length of the pendulum for both angles.