a 2.5 kg mass is connected to a spring. when a 4N is applied to the spring it compresses 2cm. if the spring is stretched and then the mass is released, what would be the period of the motion.

To find the period of the motion, we need to determine the stiffness constant (k) of the spring. We can use Hooke's Law, which states that the force applied to a spring is directly proportional to its displacement.

According to Hooke's Law, the force applied to the spring (F) is given by:

F = kx

Where F is the force, k is the stiffness constant, and x is the displacement of the spring.

In this case, we know that when a force of 4N is applied to the spring, it compresses by 2cm (0.02m). Therefore, we can plug these values into the equation:

4N = k * 0.02m

Now we can solve for k:

k = 4N / 0.02m
k = 200 N/m

With the stiffness constant determined, we can calculate the period of motion using the formula:

T = 2π√(m / k)

Where T is the period, m is the mass, and k is the stiffness constant.

In this case, the mass is given as 2.5 kg, so we can substitute the values:

T = 2π√(2.5 kg / 200 N/m)
T = 2π√(0.0125 kg/N)
T ≈ 2π * 0.1118 s
T ≈ 0.7027 s

Therefore, the period of motion is approximately 0.7027 seconds.