Insert a \"Mathematical Equation\" entry to write the formula for the following
ID: 1498400 • Letter: I
Question
Insert a "Mathematical Equation" entry to write the formula for the following quantities: The position (x) of an object moving following simple harmonic motion during an interval of time (t). The velocity (v) of an object moving following simple harmonic motion during an interval of time (t). The acceleration (a) of an object moving following simple harmonic motion during an interval of time (t). The maximum potential energy that a system of a spring with a mass can have. The maximum kinetic energy that a system of a spring with a mass can have. The angular frequency given by a system of a spring with a mass. The force exerted by a spring with constant k over a mass that pulls the spring for a small distance (delta x).Explanation / Answer
A :- maximum amplitude, w = angular frequency and phi = phase k = spring constant
1) X = Asin(wt + phi)
2) v = Awcos(wt + phi)
3) a = -Aw^2sin(wt+phi)
4) P.E = 0.5*k*A^2
5) K.E = 0.5*k*A^2 = 0.5*m*(Aw)^2
6) From abouve equation w = sqrt(k/m)
7) F = -kX