Question

Problem 3. (a) Write the equation of motion (Newton's 2nd Law where the net force on the mass is the spring force) for a mass m on a spring with spring constant k that can oscillate along a horizontal frictionless surface. Take the positive direction of the x-axis to the right. Note: The 2nd law is a 2nd-order ordinary differential equation, so your answer should include the 2nd derivative with respect to time of the displacement $x(t)$ of the mass. (b) Show by appropriate differentiation and substitution into the equation of motion above, that $x(t) = Acos(\omega t + \phi)$ is indeed a solution, with $\omega = \sqrt{k/m}$, and $\phi$ is a phase constant. (c) What is the energy of the oscillator when the spring is stretched to a length A? (d) What is the maximum velocity of the mass? (e) What is the frequency of oscillation in Hz?

          Problem 3. (a) Write the equation of motion (Newton's 2nd Law where the net force on the mass
is the spring force) for a mass m on a spring with spring constant k that can oscillate along a
horizontal frictionless surface. Take the positive direction of the x-axis to the right. Note: The 2nd
law is a 2nd-order ordinary differential equation, so your answer should include the 2nd derivative
with respect to time of the displacement $x(t)$ of the mass.
(b) Show by appropriate differentiation and substitution into the equation of motion above, that
$x(t) = Acos(\omega t + \phi)$ is indeed a solution, with $\omega = \sqrt{k/m}$, and $\phi$ is a phase constant.
(c) What is the energy of the oscillator when the spring is stretched to a length A?
(d) What is the maximum velocity of the mass?
(e) What is the frequency of oscillation in Hz?

Problem 3. (a) Write the equation of motion (Newton's 2nd Law where the net force on the mass
is the spring force) for a mass m on a spring with spring constant k that can oscillate along a
horizontal frictionless surface. Take the positive direction of the x-axis to the right. Note: The 2nd
law is a 2nd-order ordinary differential equation, so your answer should include the 2nd derivative
with respect to time of the displacement x(t) of the mass.
(b) Show by appropriate differentiation and substitution into the equation of motion above, that
x(t) = Acos(ω t + ϕ) is indeed a solution, with ω = √(k/m), and ϕ is a phase constant.
(c) What is the energy of the oscillator when the spring is stretched to a length A?
(d) What is the maximum velocity of the mass?
(e) What is the frequency of oscillation in Hz?

Added by Lori Y.

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