Simple harmonic motion , Particle

[EvilBunny]

Homework Statement

A 150 grams particle oscillating in SHM travels 24 cm between the two extreme points in its motion with an average speed of 60cm/s

Find
a) angular frequency
b) the maximum force on the particle
C) the maximum speed

The Attempt at a Solution

My first question would be what approach to use ?? This is the first problem I do with a particle. I am having trouble just finding the angular frequency and I don't even know if am suppose to use the weight for the first answer.

My second question is , what do they mean by maximum force on the particle ?
is it somewhat like a spring Fsp = kx ?

 

[tiny-tim]

A 150 grams particle oscillating in SHM travels 24 cm between the two extreme points in its motion with an average speed of 60cm/s

Find
a) angular frequency
b) the maximum force on the particle
C) the maximum speed

Hi EvilBunny!

SHM means the acceleration is proportional to (minus) the distance …

x'' = -kx.

You should be able to get everything from that (and no, you only need the weight for part b).

 

[baba89]

Hello, it seems like you are having some trouble with this problem. Let's break it down step by step. First, let's define simple harmonic motion (SHM) and a particle.

Simple harmonic motion is a type of periodic motion in which an object moves back and forth between two points, with the same amount of time between each point. This motion is characterized by a restoring force that is directly proportional to the displacement of the object from its equilibrium position. This means that the further the object is from its equilibrium point, the stronger the restoring force will be, pulling the object back towards its equilibrium position.

A particle, in this context, refers to a small, point-like object that has mass but no size. In this problem, the particle has a mass of 150 grams, which we can convert to kilograms by dividing by 1000. So the mass of the particle is 0.150 kg.

Now, let's address the questions.

a) To find the angular frequency, we can use the formula w = 2π/T, where w is the angular frequency and T is the period of the motion. In this problem, we are given the distance traveled by the particle (24 cm) and the average speed (60 cm/s). Remember that speed is a measure of how fast something is moving, while velocity is a measure of how fast something is moving in a specific direction. Since the particle is moving back and forth between two points, its velocity will change direction at each point, but its speed will remain constant. This means that the average speed is equal to the maximum speed, and we can use this value to find the period of the motion.

The period of the motion can be found using the formula T = 2π/w. Substituting in our known values, we get:

60 cm/s = 2π/w
w = 2π/(60 cm/s)
w = 2π * 100 s/cm
w = 200π s^-1

So the angular frequency of the particle is 200π s^-1.

b) To find the maximum force on the particle, we can use the formula F = -kx, where F is the force, k is the spring constant, and x is the displacement from equilibrium. In this problem, we are not given the spring constant, but we can use the formula for the period (T = 2π√(