Question

There is a pendulum with a length of 5m and a mass on the end of 120kg, the gravity is 10m/s2. Can the pendulum reach one side to the other in three seconds?

Answer 1

Answer on Question #49804, Physics, Mechanics | Kinematics | Dynamics |

Question:

There is a pendulum with a length of 5m and a mass on the end of 120kg, the gravity is 10m/s². Can the pendulum reach one side to the other in three seconds?

Solution:

Fig. 1

If deviation from the equilibrium position small ($\theta << 1$), the period of the motion, the time for a complete oscillation is $T$ given by Eq. (1) (see Fig. 1).

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

where $g$ is acceleration due to gravity, $L$ is the length of the pendulum.

The time needed for pendulum to reach from one side to the other is given by Eq.(2).

$$t = T / 2 = \pi \sqrt {\frac {L}{g}} = 3.14 \sqrt {\frac {5 m}{10 m / s ^ {2}}} = 2.22 s$$ $$t = 2.22 s < 3 s$$

Answer:

The pendulum can reach from one side to the other in three seconds.