In Concept Simulation 10.2 you can explore the concepts that are important in this problem. Astronauts on a distant planet set up a simple pendulum of length 1.20 m. The pendulum executes simple harmonic motion and makes 100 complete oscillations in 290 s. What is the magnitude of the acceleration due to gravity on this planet

5.63m/s2

Explanation:

Step 1:

Data obtained from the question.

Length (L) = 1.20 m

Time (t) = 290 seconds

Number of oscillation (n) = 100

Period (T) = ?

Acceleration due to gravity (g) = ?

Step 2:

Determination of the period. This is illustrated below:

Period is the time taken to make one complete oscillation. It is given by:

Period (T) = time (t) / number of oscillation (n)

T = t/n

t = 290 secs

n = 100

T = t/n

T = 290/100

T = 2.9 secs

Step 3:

Determination of the acceleration due to gravity of the planet. This is illustrated below:

Applying the equation T = 2π√ (L/g), the value of 'g' can be obtained as follow:

T = 2π√ (L/g)

T = 2.9 secs

L = 1.20 m

g = ?

T = 2π√ (L/g)

2.9 = 2π√ (1.2/g)

Take the square of both side

8.41 = 4π^2 (1.2/g)

8.41 = 4.8π^2 / g

Cross multiply to express in linear form

8.41 x g = 4.8π^2

Divide both side by 8.41

g = 4.8π^2/8.41

g = 5.63m/s2

Therefore, the acceleration due to gravity of the planet is 5.63m/s2