Related questions
Question
![**Spring-Mass System Analysis**
A 1.70 kg mass on a spring has displacement as a function of time given by the equation:
\[ x(t) = (7.40 \, \text{cm}) \cos \left( (4.16 \, \text{rad/s}) \, t - 2.42 \, \text{rad} \right) \]
For related problem-solving tips and strategies, you may want to view a Video Tutor Solution on Angular frequency, frequency, and period in simple harmonic motion.
---
### Exercises
**Part A:**
**Objective:** Find the time for one complete vibration.
**Instructions:** Express your answer with the appropriate units.
\[ T = \,\_\_\_\_ \, \text{Units} \]
**Part B:**
**Objective:** Find the force constant of the spring.
**Instructions:** Express your answer with the appropriate units.
\[ k = \,\_\_\_\_ \, \text{Units} \]
**Part C:**
**Objective:** Find the maximum speed of the mass.
**Instructions:** Express your answer with the appropriate units.
\[ v_{\text{max}} = \,\_\_\_\_ \, \text{Units} \]
---
Each section provides a field for your answer, and you can submit your response to verify its correctness. Use the appropriate buttons for formatting or requesting additional hints.](https://content.bartleby.com/qna-images/question/2e0c671f-6d07-45cf-8505-b36fe395c45a/b42a019c-b153-44b2-8aa6-f11a920f46ca/v4j957p_processed.png)
Transcribed Image Text:**Spring-Mass System Analysis**
A 1.70 kg mass on a spring has displacement as a function of time given by the equation:
\[ x(t) = (7.40 \, \text{cm}) \cos \left( (4.16 \, \text{rad/s}) \, t - 2.42 \, \text{rad} \right) \]
For related problem-solving tips and strategies, you may want to view a Video Tutor Solution on Angular frequency, frequency, and period in simple harmonic motion.
---
### Exercises
**Part A:**
**Objective:** Find the time for one complete vibration.
**Instructions:** Express your answer with the appropriate units.
\[ T = \,\_\_\_\_ \, \text{Units} \]
**Part B:**
**Objective:** Find the force constant of the spring.
**Instructions:** Express your answer with the appropriate units.
\[ k = \,\_\_\_\_ \, \text{Units} \]
**Part C:**
**Objective:** Find the maximum speed of the mass.
**Instructions:** Express your answer with the appropriate units.
\[ v_{\text{max}} = \,\_\_\_\_ \, \text{Units} \]
---
Each section provides a field for your answer, and you can submit your response to verify its correctness. Use the appropriate buttons for formatting or requesting additional hints.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 2 steps with 1 images
Knowledge Booster
Similar questions
- Problem HW7.2 A block of mass m = 1.8 kg is fastened to an unstrained horizontal spring whose spring constant is k = 85 N/m. The block is given a displacement of +0.15 m, where the sign indicates that the displacement is along the +x-axis, and then released from rest. (a) Find the angular frequency of the resulting oscillatory motion. Does this number change if the initial displacement is larger? Explain with a sentence or two. (b) Use concept of energy to determine the maximum speed of the block. Explicitly state which initial and final positions you used for energy states. (c) Use the concept of force to set up a free body diagram and Newton's Second Law equation to determine the magnitude of the maximum acceleration of the block.arrow_forwardA 330-kg wooden raft floats on a lake. When a 70-kg man stands on the raft, it sinks 3.9 cm deeper into the water. When he steps ff, the raft oscillates for a while. Part A What is the frequency of oscillation? Express your answer using two significant figures. Η ΑΣφ Hz Submit Request Answer Part B What is the total energy of oscillation (ignoring damping)?arrow_forwardA small earthquake starts a lamppost vibrating back and forth. The amplitude of the vibration of the top of the lamppost is 7.0 cm at the moment the quake stops, and 7.2 s later it is 1.6 cm. Part A What is the time constant for the damping of the oscillation? Express your answer with the appropriate units. HÅ T = Submit Request Answer Part B Value A= What was the amplitude of the oscillation 3.6 s after the quake stopped? Express your answer with the appropriate units. Submit HÅ Value Units Request Answer ? Units ?arrow_forward
- Robert receives a parking ticket. Angry, he punches the No Parking sign with a constant force of 500 N, displacing the sign by 5.0 cm. The sign swings back and forth in SHM(simple harmonic motion) with a frequency of 4.5 Hz (4.5 cycles per second). i. Assuming he ends his punch at time t = 0 with the sign at rest at a position x = −5.0 cm, write an equation for the position of the sign as a function of time. ii. What is the maximum speed? iii. What is the effective spring constant (or stiffness constant) of the No Parking sign?arrow_forwardHelp me with this question, please, only typingarrow_forwardChapter 15, Problem 014 A simple harmonic oscillator consists of a block of mass 1.40 kg attached to a spring of spring constant 350 N/m. When t 0.700 s, the position and velocity of the block are x oscillations? What were the (b) position and (c) velocity of the block at t 0 s? 0.115 m and v = 3.600 m/s. (a) What is the amplitude of the (a) Number Units (b) Number Units (c) Number Unitsarrow_forward
- Imagine an idealized mass-spring system. It is vibrating with a certain amplitude. If we keep the same spring and vibration amplitude but double the mass, what happens to the mechanical energy of the system? O It increases by a factor of 2. O It increases by a factor of V2. O It increases by a factor of 3. O It does not change. O It increases by a factor of 4.arrow_forwardA block is on a horizontal surface (a shake table) that is moving back and forth horizontally with simple harmonic motion of frequency 2.44 Hz. The coefficient of static friction between block and surface is 0.373. How great can the amplitude of the SHM be if the block is not to slip along the surface? Number i Unitsarrow_forwardConsider an ideal spring with spring constant k = 20 N/m. The spring is attached to an object of mass m = 2.0 kg that lies on a horizontal frictionless surface. The spring-mass system is compressed a distance xo = 50 cm from equilibrium and then released with an initial speed vo= 0 m/s toward the equilibrium position. x=0 equilibrium initial state a. What is the period of oscillation for this system? b. Starting at t = 0, how long will it take for the object to first return to the equilibrium position?arrow_forward
- An object is undergoing SHM with period 0.750s and amplitude 0.320 m. At t = 0, the object is at r = 0.320 m and is instantaneously at rest. Part A You may want to review (Page). For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of Angular frequency, frequency, and period in shm. Calculate the time it takes the object to go from z = 0.320 m, to x = 0.160 m. Express your answer with the appropriate units. ? t = 0.1875 Is Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining Part B Calculate the time it takes the object to go from x = 0.160 m, to z =0. Express your answer with the appropriate units. HA ? t = 0.125 S Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining MacBook Air esc 80 000 F1 F2 F3 DII F4 DD F5 F6 F7 FB F9 F10arrow_forwardA block is on a horizontal surface (a shake table) that is moving back and forth horizontally with simple harmonic motion of frequency 1.00 Hz. The coefficient of static friction between block and surface is 0.425. How great can the amplitude of the SHM be if the block is not to slip along the surface? Number Unitsarrow_forward
arrow_back_ios
arrow_forward_ios