Logo
Home Study Material Contact Search
AI Chat FREE
  1. sciences
  2. physics
  3. the 11 g head of a bobble-head doll oscillates in

The 11 g head of a bobble-head doll oscillates in SHM at a frequency of 5.0...

Free

80.2K

Verified Solution

Question

Physics

The 11 g head of a bobble-head doll oscillates in SHM at afrequency of 5.0 Hz .

What is the spring constant of the spring on which the head ismounted?

Suppose the head is pushed ‎2.0 cm against the spring, thenreleased. The amplitude of the head's oscillations decreases to0.5cm in 4.0s. What is the head's damping constant?

Ive asked this question multiple times and nobody can get itright.

Answer & Explanation Solved by verified expert
3.9 Ratings (538 Votes)

A)

Given

Mass of the head, m = 0.011 kg

Frequency of the oscillation, f = 5.0 Hz

From the relation, f = (1/2π) √k/m

5 = 1/(2pi)*sqrt(k/0.011)

from here K =10.8566 N/m

The maximum speed , vmax = xmω

The amplitude ,  xm     = 0.02 m

Angular frequency , ω = √k / m = sqrt( 10.8566/0.011) = 31.4159774 rad/s

vmax = xmω = 0.02* 31.4159774 = 0.628319548 m/s

B)

The oscillations decreases to 0.5 cm in t = 4.0s, the damping constant b is

    calculated from the relation

                                  x(t)   =    xm e -bt/2m

0.005  m = (0.02 m) e -bt/2m  ​

-bt / 2m = ln(0.25)

= -b*4 /( 2*0.011) = -1.3862

  b = 0.0076241 kg/s

  

am i right ?
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Chemistry
1.2K views

Select all of the following equations that would most likely give a positive value for ΔS....

Chemistry
1.2K views

Rank these compounds from weakest base to strongest base. A)4-methylaniline B)aniline C)trifluoromethyl aniline

Economics
1.2K views

Ecopower produces power in New York City according to a cost function of C(Q) = Q^2....

Physics
1.2K views

2012 1 Two ideal diodes are connected to a battery as shown in the circuit...

Physics
1.2K views

ply supported beam of span 4m ted to an anticlockwise couple m at the center...

Geometry
1.2K views

Lesson 5 4 Checkpoint below Once you have completed the above problems and checked your...

Basic Math
1.2K views

The infectivity of a certain pathogen is quantified by measuring the area between two curves....

Calculus
1.2K views

1 point Use cylindrical coordinates to evaluate the triple integral z 1 9 x y...

Algebra
1.2K views

7 What is the y intercept in the equation y 45x 65

Accounting
1.2K views

5. What is the future value of a two...

Accounting
1.2K views

Butrico Manufacturing Corporation uses a standard cost system, records materials price variances when direct materials...

Accounting
1.2K views

EXPLAIN THE GIVEN DATA AND EXPRESS EXACTLY BY HOW MUCH DOES EACH INDEPENDENT VARIABLE MATTER?...