Equation of x(t) for a certain point moving with SHM

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• Given x(t) for a certain SHM, find x, v, and a at a given instant.

  18328 Given x(t) for a certain SHM, find x, v, and a at a given instant. For a certain point executing SHM on an x axis with amplitude .40 m, the equation giving its location as a function of time is given by: (1) x = .4 m cos (6 t) a.

• SHM equations from the motion of a point moving in a circle

  ABOVE EQUATION (1) is x(t), (2) is v(t) and (3) is a(t), the general equations of SHM for a point which starts at +Xm and moves between +Xm and -Xm on the x axis.

• A Standing wave is the sum of two given waves on a wire. Write its equation.

  See ATTACHMENT #1 for an example of two such waves on a wire. Following the example, you should find: (1) y= .30 (sin 5x )(cos 3 Pi t) Notice that at a certain value of x, say .8 m, the equation shows SHM for that point. PART b.

• Moving mass m collides with stationary mass M attached to a spring on a frictionless table. Write SHM equations.

  6969 Moving mass m collides with stationary mass M attached to a spring on a frictionless table. Write SHM equations. SEE ATTACHMENT #1 for a diagram of parameters and a reference circle.

• After a block and marble collide, the block executes SHM

  A general equation giving x(t) for a SHM is: (2) x = Xm cos( w t + Q) in which w is the angular frequency and Q is the initial phase angle when t =0. Step 1.

• Simple Harmonic Motion Mass Hanging Spring.

  The general expression giving x(t) for a body moving with SHM is: (1) x = Xm cos (w t + Q) in which w is the angular frequency in rad/sec, Q is the initial phase angle, and Xm is the amplitude. Step 2.

• traveling wave equation obtain much information about the wave.

  For a point which is at x1= 2.4 m from the origin, write y(x1, t) with numbers and units for constants, for the SHM of that point, and find the maximum velocity of that point. Physics statements: A.

• Kinematics calculations using derivatives

  A general equation giving the x coordinate of a body moving with SHM on an x axis between +Xm and -Xm, with the x axis origin at the center of motion, angular frequency w, and initial phase angle Q in radians, is: (1) x= Xm sin( w t + Q) B.

• Equations of SHM of a mass attached to a spring on a horizontal frictionless table.

  (HINT: This equation is a second order differential equation. One solution for it is of the form (2) x= A cos (omega t) in which constants A, and (omega) must be found in terms of given parameters k and M. PART b.