1-17. The motion of macroscopic particles is governed by Newton's equation of motion, which can be...

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1-17. The motion of macroscopic particles is governed by Newton's equation of motion, which can be written in the form dx m = f(x) di (1) where x(t) is the position of the mass m and f(x) is the force acting on the particle. Equation 1 is a differential equation whose solution gives x(t), the trajectory of the mass. In the case of a harmonic oscillator, m is the reduced mass and f(x) = -kx (Hooke's law), so that Newton's equation is H- dx = -k.x di Show that x(t) = A cos 2 vt satisfies this equation if v = (1/2)(k/u). This result is valid only for a macroscopic oscillator, called a classical harmonic oscillator. 1-17. The motion of macroscopic particles is governed by Newton's equation of motion, which can be written in the form dx m = f(x) di (1) where x(t) is the position of the mass m and f(x) is the force acting on the particle. Equation 1 is a differential equation whose solution gives x(t), the trajectory of the mass. In the case of a harmonic oscillator, m is the reduced mass and f(x) = -kx (Hooke's law), so that Newton's equation is H- dx = -k.x di Show that x(t) = A cos 2 vt satisfies this equation if v = (1/2)(k/u). This result is valid only for a macroscopic oscillator, called a classical harmonic oscillator.