Question

A machine part is modeled as a pendulum connected to a spring as illustrated in Figure below. Ignore the mass of pendulum's rod and assume that the rotation is small enough so that the spring only deflects horizontally. a) Derive the equation of motion. b) Calculate the system natural frequency c) What is the solution for this system (response)?

          A machine part is modeled as a pendulum connected to a spring as illustrated in Figure
below. Ignore the mass of pendulum's rod and assume that the rotation is small enough so that the
spring only deflects horizontally.
a) Derive the equation of motion.
b) Calculate the system natural frequency
c) What is the solution for this system (response)?

A machine part is modeled as a pendulum connected to a spring as illustrated in Figure
below. Ignore the mass of pendulum's rod and assume that the rotation is small enough so that the
spring only deflects horizontally.
a) Derive the equation of motion.
b) Calculate the system natural frequency
c) What is the solution for this system (response)?

Added by Sean M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

08/14/2023

Step 1

There are three main forces: - Gravitational force: mg acting downward - Spring force: k·x acting horizontally (where x is the horizontal displacement) - Tension in the rod: acting along the direction of the rod Show more…

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A machine part is modeled as a pendulum connected to a spring as illustrated in Figure below. Ignore the mass of pendulum's rod and assume that the rotation is small enough so that the spring only deflects horizontally. 0 k g m a) Derive the equation of motion. b) Calculate the system natural frequency c) What is the solution for this system (response)?