In the first case, the force acting on the spring is the weight of the mass:

This force causes a stretching of

on the spring, so we can use these data to find the spring constant:

In the second case, the first mass is replaced with a second mass, whose weight is

And since we know the spring constant, we can calculate the new elongation of the spring:
The period T of a pendulum is given by:

where L is the length of the pendulum while

is the gravitational acceleration.
In the pendulum of the problem, one complete vibration takes exactly 0.200 s, this means its period is

. Using this data, we can solve the previous formula to find L:
Initial speed is less than final speed
Answer:
The force is 
Explanation:
The diagram for this question is shown on the first uploaded image
From the question we are told that
The weight of the gate is 
The vertical component of F is 
From the diagram , taking moment about the pivot we have

Where
is the weight of the gate evaluated as

=> 
=> 
=> 