angular frequency is the [rad.s-1] initial phase angle is the (value of the phase angle at = 0) [rad]. Its value t determines the initial displacement of the particle = 0, t (3) Equation (2) can also be written as: A sine function A sine and cosine function The values of the constants , and can be determined from the initial xmax, A B ’, conditions (x and at time = 0). v t = 1 m = 0 rad = 1 m = - /2 rad xmax xmax = 20 s = 0.05 Hz = 0.3142 rad.s-1 = 20 s = 0.05 Hz = 0.3142 rad.s-1 T f T f = 1 m = /2 rad = 1 m = rad xmax xmax = 20 s = 0.05 Hz = 0.3142 rad.s-1 = 20 s = 0.05 Hz = 0.3142 rad.s-1 T f T f = 0.5 m = / 4 rad = 0.75 m = - / 4 rad xmax xmax = 20 s = 0.05 Hz = 0.3142 rad.s-1 = 40 s = 0.025 Hz = 0.1571 rad.s-1 T f T f The velocity is the time derivative of the displacement v (4) The displacement and velocity are /2 rad out of phase with each other The velocity amplitude is (always a positive number) acceleration The is the time derivative of the velocity a (5) The acceleration amplitude is (always a positive number)
is the angular frequency [rad.s-1] is the initial phase angle (value of the phase angle at t = 0) [rad]. Its value determines the initial displacement of the particle t = 0, (3) Equation (2) can also be written as: A sine function A sine and cosine function The values of the constants xmax, , ’, A and B can be determined from the initial conditions (x and v at time t = 0). xmax = 1 m = 0 rad T = 20 s f = 0.05 Hz = 0.3142 rad.s-1 xmax = 1 m = - /2 rad T = 20 s f = 0.05 Hz = 0.3142 rad.s-1 xmax = 1 m = /2 rad T = 20 s f = 0.05 Hz = 0.3142 rad.s-1 xmax = 1 m = rad T = 20 s f = 0.05 Hz = 0.3142 rad.s-1 xmax = 0.5 m = / 4 rad T = 20 s f = 0.05 Hz = 0.3142 rad.s-1 xmax = 0.75 m = - / 4 rad T = 40 s f = 0.025 Hz = 0.1571 rad.s-1 The velocity v is the time derivative of the displacement (4) The displacement and velocity are /2 rad out of phase with each other The velocity amplitude is (always a positive number) The acceleration a is the time derivative of the velocity (5) The acceleration amplitude is (always a positive number)