Given this you can find A and phi just from the initial conditions. I suggest that you write them down. You will then have two equations and two unknowns which can be solved.martinbandung said:
Is this the entirety of the information you are given? No block mass or spring constant?martinbandung said:
The information is sufficient. The mass and spring constant are only relevant for computing the angular frequency, which has already been given.gneill said:
The simple harmonic equation is a mathematical representation of the motion of a system undergoing simple harmonic motion. It is typically written as x(t) = A sin(ωt + φ), where x(t) is the position of the system at time t, A is the amplitude, ω is the angular frequency, and φ is the phase angle.
Simple harmonic motion is a type of periodic motion in which the restoring force is directly proportional to the displacement of the system from its equilibrium position. This results in a sinusoidal motion, where the system oscillates back and forth around its equilibrium position.
The key characteristics of simple harmonic motion include a constant amplitude, a constant period, a sinusoidal motion, and a constant frequency. It is also characterized by the presence of a restoring force that is proportional to the displacement of the system from its equilibrium position.
Some examples of simple harmonic motion in everyday life include the motion of a pendulum, the vibration of a guitar string, and the motion of a mass on a spring. Other examples include the motion of a swing, the motion of a tuning fork, and the motion of a mass attached to a rubber band.
The simple harmonic equation is used in various fields of science and engineering to model and analyze systems that undergo simple harmonic motion. This includes applications in fields such as physics, mechanics, electrical engineering, and acoustics. It is also used to design and optimize systems that involve simple harmonic motion, such as musical instruments and shock absorbers.
