Final answer:
The force exerted by a spring on a mass during simple harmonic motion is determined by the restoring force, described by Hooke's Law. However, without the spring constant, we must use the relationship between maximum acceleration and amplitude. The exact force at a given time can be found through the acceleration as a function of time and applying Newton's second law.
Step-by-step explanation:
To find the force that a spring puts on a mass 3.3 seconds after it is released, one must understand the physics principles involved in simple harmonic motion (SHM). A 1.14 kg mass with a frequency of 20 Hz and an amplitude of 1.2 m is oscillating in SHM. The restoring force in SHM is given by Hooke's law, which states F = -kx, where k is the spring constant and x is the displacement from the equilibrium position.
However, without the spring constant value, we cannot directly calculate the force. Since the question does not provide the spring constant, we can use the relationship between maximum acceleration (a_max) and amplitude (A) in SHM, which is a_max = (2πf)^2 × A, where f is the frequency. We can then use Newton's second law (F = ma) to find the maximum force at the point of maximum displacement. Nevertheless, we are asked to find the force at a specific time, for which we need the acceleration at that time point. We can find the acceleration as a function of time a(t) = -A(2πf)^2cos(2πft), and then plug in the time t = 3.3 s to find the specific force at that time.