# Simple harmonic motion for block of mass

• phazei
In summary: The question should specify whether the original position refers to the equilibrium position or the initial position. In summary, the problem gives a block of mass m attached to a spring with spring constant k, pulled to the right a distance A and released at t=0 with zero initial velocity. It asks for the time t_1 when the block returns to its original position, which is either the equilibrium position or the initial position. The correct answer is t_1 = (pi/2)(m/k)^(1/2).
phazei
the problem gives
x(t)= A cos( (k/m)^(1/2) * t)

A block of mass m is attached to a spring whose spring constant is k. The other end of the spring is fixed so that when the spring is unstretched, the mass is located at x=0. View Figure . Assume that the +x direction is to the right.

The mass is now pulled to the right a distance A beyond the equilibrium position and released, at time t=0, with zero initial velocity.

At what time t_1 does the block come back to its original position for the first time?

So when t=0
cos( (k/m)^(1/2) * 0) = 1

so at t_1
cos( (k/m)^(1/2) * t_1) = 1

so
(k/m)^(1/2) * t_1 = 2pi

so t_1 = 2pi(m/k)^(1/2)

but when i submit it it says it's off by a multiplicative factor!

what's wrong with that?

thanks,

That's funky. $T=2\pi\sqrt{\frac{m}{k}}$ is correct as you can easily check.

sigh. apparently the original position it was referring to was the equalibrium position, not the position it was initially pulled to.
So cos has to be solved to equal 0.

cos( (k/m)^(1/2) * t) = 0

t_1 = (pi/2)(m/k)^(1/2)

I think the wording is poorly chosen.

## What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object moves back and forth in a straight line, with a restoring force that is directly proportional to its displacement from equilibrium.

## What is a block of mass in simple harmonic motion?

A block of mass is an object with a known mass that is subject to a restoring force, causing it to undergo simple harmonic motion.

## What factors affect the period of a block of mass in simple harmonic motion?

The period of a block of mass in simple harmonic motion is affected by the mass of the object, the spring constant of the restoring force, and the amplitude of the motion.

## How is the amplitude of simple harmonic motion determined?

The amplitude of simple harmonic motion is determined by the maximum displacement of the object from equilibrium. It is directly related to the energy of the system, with larger amplitudes corresponding to higher energy levels.

## What are some real-life examples of simple harmonic motion for a block of mass?

Some real-life examples of simple harmonic motion for a block of mass include a pendulum, a mass on a spring, and a vibrating guitar string.

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