A cart with mass m=4.2 kg is moving on a frictionless surface. One end of the cart is attached to a spring, the other end of which is attached to a rigid wall. There is no other force exerted on the cart besides the spring force, and the cart follows simple harmonic motion. When the spring is at its equilibruim position, the carat is moving at the speed of 2.1 m/s and the spring can stretch or be compressed as far as 15 cm from the equilibruim position during this simple harmonic motion. What is the amplitude of a carts simple harmonic motion? What is the spring constant of the spring? What is the period of this simple harmonic motion? What is the maximum acceleration of the cart? What is the speed of the cart when it is 10 cm away from the equilibrium position of the spring?
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
A cart with mass m=4.2 kg is moving on a frictionless surface. One end of the cart is attached to a spring, the other end of which is attached to a rigid wall. There is no other force exerted on the cart besides the spring force, and the cart follows simple harmonic motion. When the spring is at its equilibruim position, the carat is moving at the speed of 2.1 m/s and the spring can stretch or be compressed as far as 15 cm from the equilibruim position during this simple harmonic motion.
What is the amplitude of a carts simple harmonic motion?
What is the spring constant of the spring?
What is the period of this simple harmonic motion?
What is the maximum acceleration of the cart?
What is the speed of the cart when it is 10 cm away from the equilibrium position of the spring?
Given
m=4.2 Kg
Vm=2.1 m/s
Am=0.15m
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
