{"id":45556,"date":"2024-04-15T21:59:42","date_gmt":"2024-04-15T21:59:42","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=45556"},"modified":"2024-04-15T21:59:42","modified_gmt":"2024-04-15T21:59:42","slug":"letxt-be-the-input-and-yt-be-the-output-of-a-continuous-time-system-match-the-system-properties-p1-p2-and-p3-with-system-relations-r1-r2-p3-p4-properties-p1-linear-but-not-time-invariant-p","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/letxt-be-the-input-and-yt-be-the-output-of-a-continuous-time-system-match-the-system-properties-p1-p2-and-p3-with-system-relations-r1-r2-p3-p4-properties-p1-linear-but-not-time-invariant-p\/","title":{"rendered":"Letx(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with system relations R1, R2, P3, P4. Properties P1 : Linear but NOT time-invariant P2 : Time-invariant but NOT linear P3 : Linear and time-invariant Relations R1 : y(t) = t2x(t) R2 : y(t) = t |x(t)| R3 : y(t) = |x(t)| R4 : y(t) = x(t &#8211; 5)"},"content":{"rendered":"<p>\r\n    <!-- Check if it's an AMP page -->\r\n            <!-- Non-AMP version -->\r\n        <div class=\"mcq-container\" data-quiz-id=\"quizState_6a978720e7d1f\">\r\n                                            <div class=\"option\" data-option-key=\"option1\" data-is-correct=\"true\">\r\n                    (P1, R1), (P2, R3), (P3, R4)                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option2\" data-is-correct=\"false\">\r\n                    (P1, R2), (P2, P3), (P3, R4)                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option3\" data-is-correct=\"false\">\r\n                    (P1, R3), (P2, R1), (P3, R2)                <\/div>\r\n                                            <div class=\"option\" data-option-key=\"option4\" data-is-correct=\"false\">\r\n                    (P1, R1), (P2, R2), (P3, R3)                <\/div>\r\n                            \r\n            <!-- Feedback messages for non-AMP -->\r\n            <div class=\"feedback\" data-feedback=\"wrong\">Answer is Right!<\/div>\r\n            <div class=\"feedback\" data-feedback=\"right\">Answer is Wrong!<\/div>\r\n        <\/div>\r\n\r\n        <script>\r\n        document.addEventListener('DOMContentLoaded', function () {\r\n            var containers = document.querySelectorAll('.mcq-container');\r\n\r\n            containers.forEach(function(container) {\r\n                var options = container.querySelectorAll('.option');\r\n                var feedbackSelect = container.querySelector('[data-feedback=\"select\"]');\r\n                var feedbackWrong = container.querySelector('[data-feedback=\"wrong\"]');\r\n                var feedbackRight = container.querySelector('[data-feedback=\"right\"]');\r\n\r\n                options.forEach(function(option) {\r\n                    option.addEventListener('click', function() {\r\n                        var selectedOption = option.getAttribute('data-option-key');\r\n                        var isCorrect = option.getAttribute('data-is-correct') === 'true';\r\n\r\n                        \/\/ Remove previous selections\r\n                        options.forEach(function(opt) {\r\n                            opt.classList.remove('correct', 'incorrect');\r\n                        });\r\n\r\n                        \/\/ Add the correct\/incorrect class\r\n                        if (isCorrect) {\r\n                            option.classList.add('correct');\r\n                            feedbackRight.hidden = false;\r\n                            feedbackWrong.hidden = true;\r\n                        } else {\r\n                            option.classList.add('incorrect');\r\n                            feedbackRight.hidden = true;\r\n                            feedbackWrong.hidden = false;\r\n                        }\r\n\r\n                        \/\/ Hide select feedback\r\n                        feedbackSelect.hidden = true;\r\n                    });\r\n                });\r\n            });\r\n        });\r\n        <\/script>\r\n    \r\n    <!--more--><\/p>\n<p>The correct answer is (P1, R1), (P2, R3), (P3, R4).<\/p>\n<p>A linear system is one that satisfies the superposition principle, which states that the output of a linear system is the sum of the outputs of the system due to each individual input. A time-invariant system is one that does not change its behavior over time.<\/p>\n<p>Property P1 is linear but not time-invariant. This means that the output of the system is the sum of the outputs of the system <div class=\"youtube-subscribe-container\">\r\n        <a href=\"https:\/\/www.youtube.com\/channel\/UCNHT8lW-JmLC68rjBfZhdkg?sub_confirmation=1\" target=\"_blank\" class=\"youtube-subscribe-button\">\r\n            <span class=\"youtube-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 576 512\">\r\n                    <path d=\"M549.7 124.1c-6.3-23.7-24.8-42.3-48.3-48.6C458.8 64 288 64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 <div class=\"telegram-channel-container\">\r\n        <a href=\"https:\/\/t.me\/pscnotes2025\" target=\"_blank\" class=\"telegram-channel-button\">\r\n            <span class=\"telegram-icon\">\r\n                <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 496 512\">\r\n                    <path fill=\"white\" d=\"M248,8C111,8,0,119,0,256s111,248,248,248s248-111,248-248S385,8,248,8z M362,177L320,367c-3,14-10,18-20,14l-56-41l-27,26 c-3,3-5,5-10,5l4-63L323,196c5-5-1-7-8-3l-98,62l-42-13c-9-3-10-9,2-14l162-63C351,160,365,164,362,177z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Join Our Telegram Channel\r\n        <\/a>\r\n    <\/div> 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z\"\/>\r\n                <\/svg>\r\n            <\/span>\r\n            Subscribe on YouTube\r\n        <\/a>\r\n    <\/div> due to each individual input, but the output depends on the time at which the input is applied. For example, if the input is $x(t)$, then the output is $y(t) = t^2x(t)$.<\/p>\n<p>Property P2 is time-invariant but not linear. This means that the output of the system does not depend on the time at which the input is applied, but the output is not the sum of the outputs of the system due to each individual input. For example, if the input is $x(t)$, then the output is $y(t) = t|x(t)|$.<\/p>\n<p>Property P3 is linear and time-invariant. This means that the output of the system is the sum of the outputs of the system due to each individual input, and the output does not depend on the time at which the input is applied. For example, if the input is $x(t)$, then the output is $y(t) = |x(t)|$.<\/p>\n<p>Relation R1 is $y(t) = t^2x(t)$. This is a linear relation, because the output is the sum of the outputs of the system due to each individual input. However, it is not time-invariant, because the output depends on the time at which the input is applied. Therefore, R1 matches with P1.<\/p>\n<p>Relation R2 is $y(t) = t|x(t)|$. This is not a linear relation, because the output is not the sum of the outputs of the system due to each individual input. However, it is time-invariant, because the output does not depend on the time at which the input is applied. Therefore, R2 matches with P2.<\/p>\n<p>Relation R3 is $y(t) = |x(t)|$. This is a linear and time-invariant relation. Therefore, R3 matches with P3.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Join Our Telegram Channel Subscribe on YouTube<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[959],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.2 (Yoast SEO v23.3) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Letx(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with system relations R1, R2, P3, P4. Properties P1 : Linear but NOT time-invariant P2 : Time-invariant but NOT linear P3 : Linear and time-invariant Relations R1 : y(t) = t2x(t) R2 : y(t) = t |x(t)| R3 : y(t) = |x(t)| R4 : y(t) = x(t - 5)<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/letxt-be-the-input-and-yt-be-the-output-of-a-continuous-time-system-match-the-system-properties-p1-p2-and-p3-with-system-relations-r1-r2-p3-p4-properties-p1-linear-but-not-time-invariant-p\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Letx(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with system relations R1, R2, P3, P4. 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