Final answer:
The amplitude of vibration is 7 cm, the spring constant is 1.178 N/cm, the speed of the mass when it is 9 cm above the tabletop is 9.75 cm/s, and the acceleration is -35.03 cm/s^2.
Step-by-step explanation:
The amplitude of vibration for a mass attached to a Hookean spring can be calculated using the formula:
Amplitude = (Highest point - Lowest point)/2
For this problem, the amplitude is (16 cm - 2 cm)/2 = 7 cm.
The spring constant can be determined using the formula:
Spring constant (k) = (2π/period)^2 * mass
Using the given period of 4.0 s and mass of 300 g (0.3 kg), the spring constant is calculated as:
(2π/4.0)^2 * 0.3 = 1.178 N/cm
The speed and acceleration of the mass when it is 9 cm above the tabletop can be determined using the equation:
v = √(k/m) * √(A^2 - x^2)
a = -k * x / m
where v is speed, k is the spring constant, m is the mass, A is the amplitude, and x is the displacement from the equilibrium position. Plugging in the values, we get:
Speed = √(1.178/0.3) * √(7^2 - 9^2) = 9.75 cm/s
Acceleration = -1.178 * 9 / 0.3 = -35.03 cm/s^2
The speed and acceleration when the mass is at its highest or lowest point will be zero.